On a day plucked from winter, with a bitter wind whipping up raw emotions under a dull grey sky, Liverpool showed further signs of promise under Brendan Rodgers but finished the match with nothing but a place in the bottom three.

They are now looking at a statistic which shows that, since the start of 2012, they have won only two of their 12 league games at Anfield. Of a possible 72 points in the same period, home and away, they have taken a mere 20. By way of contrast, Sunday's visitors have amassed 56 points in the same period, from an identical number of fixtures.

In the aftermath of the penalty with which Robin van Persie completed the scoreline, Manchester United's fans directed a chant of "You're getting sacked in the morning" at the Liverpool manager. The response from the Kop was instant. "There's only one Brendan Rodgers," they sang. Pride was involved, of course, but perhaps they do indeed see their present plight as the darkness before the dawn.

Rodgers certainly does. "The better side lost today," he said. "In the areas we could control, I thought we were outstanding." He disputed the pivotal sending-off of Jonjo Shelvey late in the first half and, less persuasively, the defeat-sealing penalty awarded against Glen Johnson for chasing back and tripping Antonio Valencia. "Very soon our luck will change, we'll do what we need to do to win matches, and we'll fly."

While Liverpool had a full complement of players on the pitch there were plenty of indications that Rodgers is getting them to play the way he wants, combining the Anfield club's traditional power game with his preferred short-passing style.

"We've got a group of young players here who can take the club forward," he said afterwards, having seen Raheem Sterling produce another encouraging performance, this time under the eye of Roy Hodgson, who made the teenager a late addition to his last England squad.

Rodgers had also given a league debut to Jesús Fernández, known as Suso, who came on for the limping Fabio Borini at half-time, and within a minute the 18-year-old Spanish forward skipped away from Paul Scholes, playing in the neat cross from which Johnson created the chance for Gerrard to give Liverpool the lead.

Gerrard's response to the goal was to point to the sky, his thoughts no doubt on his late cousin, Jon-Paul Gilhooley, who died in the Hillsborough disaster, aged 10. As a moment of deep emotion, it compared to the one witnessed at Stamford Bridge four years ago when Frank Lampard steeled himself to convert a crucial Champions League penalty – against Liverpool, as it happens – in the week of his mother's death.

The impeccable buildup to this highly charged occasion had featured a joint television interview by Rodgers and Sir Alex Ferguson, the presentation of a bouquet of red roses from Sir Bobby Charlton to Ian Rush, a handshake between Luis Suárez and Patrice Evra, and the sight of the two captains, Gerrard and Ryan Giggs, releasing 96 balloons in commemoration of the Hillsborough victims. While the home fans sang You'll Never Walk Alone with a special intensity, United's fans responded with their own war cries, a gesture that teetered on the brink of unacceptability.

Once the match got under way, ears were cocked for the sound of old hatreds. After a subdued and disjointed opening, however, most of the harshness was reserved for events on the pitch, where the weight of the collisions and the stridency of the appeals gradually rose throughout the first half until, in the 39th minute, Mark Halsey made the decision that shaped the match.

Liverpool had worked hard to conquer their nerves and establish an definite ascendancy over a curiously disjointed United when Shelvey muscled Giggs out of possession and chased the loose ball into a second challenge with Jonny Evans. As the players slid towards each other, neither of them in full control of his action, Halsey's angle of vision persuaded him that Shelvey's part in the collision deserved a straight dismissal.

Replays suggested that a yellow card apiece might have been a more sensible conclusion, but Halsey could only go on what he believed he had seen. It was a shame for the contest, for Liverpool, and particularly for the 20-year-old Shelvey, who left the pitch in a storm of rancour. His game has much more to it than his obvious athleticism and his appetite for the ball in the Liverpool midfield seems to take a little of the pressure off Gerrard, allowing the captain to distribute the ball in a more relaxed manner.

What Liverpool really need, however, is for Suárez to rediscover the goalscoring instinct that brought him 81 league goals in 110 appearances for Ajax and 28 in 54 matches with Uruguay.

As committed to Sunday's contest as any player on view, he showed the potential to link effectively with Borini and Sterling, although he had only one decent chance to show for it, when Anders Lindegaard dived to push away his low left-foot shot on the hour.

But his endless complaining tries the patience of officials. As we saw, referees are only human, and Halsey denied him what looked like a reasonable claim for a late penalty. It is a lesson Suárez needs to learn if he is to play his part in a Liverpool revival.