An apology has been coaxed out of Luis Suárez, closely followed by one from Kenny Dalglish, but English football is unlikely to put the matter that provoked their contrition so easily out of mind. In refusing to shake the offered hand of Patrice Evra at Old Trafford on Saturday, with every camera in the stadium upon them, the Uruguayan striker released the darker emotions roiling beneath the game's prosperous surface, exposing a disturbing volatility.

Finally, after piling blunder upon blunder for four months, the public relations team at Liverpool got something right. But so turbulent a relationship could deteriorate again in an instant of flaring anger, and it remains a relief that, following three increasingly fractious encounters this season, Liverpool and Manchester United will not be meeting again in the present campaign. Football fans have long memories and a disinclination to forgive their rivals, and the first encounter between the two next season will be closely scrutinised.

The words of Suárez's statement are adequate enough but the sincerity behind them will be widely doubted, and not only in Manchester, given the player's previous attitude and the resentful response of his club to anyone who questioned his innocence. Nor, even at this stage, does he admit guilt over anything other than refusing the handshake. The ill-will festering between the two players over their contrasting accounts of what was said between them at Anfield on 15 October last year, and Suárez's issues with the 115-page document published by the FA tribunal, have not been addressed. Dalglish's statement expresses contrition for his ill-mannered exchange with a television reporter after the game.

After months of skirmishes, the events of Saturday provoked a sudden escalation of what had previously existed merely as a profound and bitter rivalry. Neither the Football Association nor the Premier League showed an inclination to step in and exert some measure of control over a deteriorating situation. The uncharacteristically emollient words of Suárez's statement may have doused the worst of the conflagration, but the embers will still be glowing. The question is whether he and his manager have done enough to divert what seemed on Saturday night like the potential deterioration of the Liverpool-United rivalry into something approaching the lethal toxicity of Scotland's Old Firm.

English football, a judge said in Southwark crown court last week, "may be thought by some to have rather lost its way". Although his reference was to the rampant greed that has overtaken the commercial side of the game, he was right in a more general sense, as we saw in the scenes before, during and after Saturday's match.

Suárez's failure to signal an end to the dispute on Saturday by reciprocating Evra's gesture unstopped the wells of poison that immediately flooded the match, the airwaves, the newsprint and – most significantly – social media. A long-standing enmity between the two most famous and powerful clubs in England had reached a new pitch of intensity, and the comments of Sir Alex Ferguson and Dalglish to the Sky Sports reporter Geoff Shreeves made it official.

Suárez, said Ferguson, was "a disgrace to Liverpool football club … The player should not be allowed to play for Liverpool again. The history that club's got, and he does that." Dalglish professed not to have seen the handshake incident, then rounded on his inquisitor for having the temerity to raise a matter that was at the forefront of everyone's mind. "I think you're bang out of order to blame Luis Suárez for anything that happened here today," he said.

It is easy to cast Liverpool as the villains here. It was Suárez, after all, who was found guilty by an FA tribunal of using racist language to insult Evra, declined to accept the findings of a painstaking inquiry, served an eight-match suspension and refused the hand of reconciliation. Even Alan Hansen, a former Liverpool hero and one of Dalglish's closest friends, roused himself to condemn the Uruguayan on Saturday night. "He's let Kenny down, he's let the club down and he's let himself down," he said, although he could not bring himself to use the Match of the Day pulpit to criticise the Liverpool manager's reaction, which followed Dalglish's tweets in support of Suárez and his sanctioning the wearing of those infamous T-shirts while the case was being heard.

But the faults are not all on one side. Evra is an easily roused character and his cavorting in celebration of Saturday's victory was, as even Ferguson noted, foolishly provocative. Copies of Red Issue, one of the most prominent United fanzines, were confiscated on Saturday when they were found to contain Ku Klux Klan masks emblazoned with the words "Suárez is innocent". And chants can be heard from the Old Trafford fans in celebration of the death of 96 Liverpool fans at Hillsborough 23 years ago. The poison and the stupidity flow both ways.

"The point about football in Britain is that it is not just a sport people take to, like cricket or tennis or running long distances," Arthur Hopcraft wrote in the introduction to The Football Man, his classic study of the game, in 1968. "It is inherent in the people. It is built into the urban psyche." It had not, he added, been "only a game" for 80 years. Little has changed in the passage of another four decades.

"The way we play the game, organise it and reward it reflects the kind of people we are," Hopcraft continued. "What happens on the football field matters, not in the way that food matters but as poetry does to some people and alcohol does to others: it engages the personality." And now that collective personality finds an additional means of expression in social media, where no comment, however judicious and even-handed its intent, goes unanswered by challenges suffused with the rage of imagined injury.

Football fans have never been paragons of balanced judgment. That is part of the fun and the release of being a fan. And even in the cloth-cap era, behaviour was not beyond reproach. In The Soccer Syndrome, the late John Moynihan recorded the message of a poster at the Den in the 1949-50 season, urging Millwall's fans not to "barrack, utter filthy abuse or molest in any manner players of the visiting team", the implicit assumption being that such things could and did happen. And that was well before the onset of hooliganism. Hopcraft wrote of Anfield: "More than any other city, Liverpool experiences its hope and its shame through football. There is no more chilling sound in the game than one of the long howls of animosity which the Liverpool crowd can drill into the ears of a visiting threat to their club's supremacy, such as Manchester United or Tottenham Hotspur."

In recent years, however, everything within English football has been turned up to boiling point, and the authorities are as much to blame in their pursuit of a mass global audience. The pre-match handshake is an example of Sky Sports' desire to dress up every one of the season's 380 Premier League fixtures as a cup final. Once upon a time players ran on to the field, took up their positions, and waited for the whistle to blow. At the end of the game they might shake an opponent's hand in acknowledgement of a satisfying contest. Now they have to put themselves through a meaningless ritual containing, as we saw on Saturday, the potential for exacerbating problems.

For the fans, anything can provide fuel for their immoderate passions. Just now it happens to be racism. An alleged outburst of racist abuse was behind the Suárez/Evra affair, and another one provoked the departure of an England manager last week. On Saturday it was announced that Micah Richards, Manchester City's 23-year-old acting captain and an England international with a dozen caps, had closed his Twitter account as a result of receiving a stream of racist messages.

This is not real racism, although it adopts its vile messages: it is a sort of play-racism, providing a convenient weapon with which to goad and even wound the adversary. The colour of Evra's or Richards's skin is less important than the colour of his shirt, which is all that it takes to inflame prejudices and distort enthusiasm into something much uglier in a game that has slipped its emotional moorings and is drifting in a sea of treacherous passions.