While one England left-back embarrasses himself when he tweets, another is only mortified when others speak. It is Leighton Baines' natural inclination to downplay his own contribution, so the paeans of praise, from his manager and opponents alike, must have been excruciating to the modest Merseysider.

"Without a doubt, he's the best left-back in the league," said the Wigan Athletic captain Gary Caldwell, ranking Baines above the man he understudies for his country, Ashley Cole. "When the left-back is their most attacking player, that shows you he must be doing something right."

While the controversial Cole's international future is the subject of speculation after the deleted message in which he called the FA "a bunch of twats", Baines represents the diplomatic, dignified antidote. Laughing, he confirmed he does not have a Twitter account: social networking is not his style. Given his instinctive understanding with Steven Pienaar, the pair scarcely need technology to communicate.

If, compared to the controversial Cole, Baines is less likely to draw attention to himself, a tour de force, capped by an expertly taken equaliser from the penalty spot, made him hard to ignore. He has become Everton's headline act and there are footballing reasons, to use the phrase Roy Hodgson deployed about Rio Ferdinand's exclusion from Euro 2012, for arguing he deserves a chance to displace Cole, as is likely for next Friday's World Cup qualifier against San Marino.

"Leighton Baines was at the heart of everything we did," said Everton's manager, David Moyes. "I thought he was extraordinary." Baines gave the impression he would rather have been deemed ordinary. "I don't know about that," said the 27-year-old, when informed of his manager's eulogy. He deployed the self-same phrase when asked if he was a rare left-back to run the game, arguing instead that Wigan's wing-back formation gave him an opportunity to get forward. "It freed me up," he said. Liberated, he prospered.

Even if only temporarily, he also lightened Moyes' mood. The trenchant Scot branded Baines's booking "a joke" and was similarly upset that Marouane Fellaini was also cautioned. Standing 6ft 4in – whether or not that includes one of football's most famous hairstyles is not recorded – the concept of the Belgian being bullied seems strange, but Moyes believes even his most intimidating player is picked on. "Fellaini needs more protection," he said.

A sense of injustice was evident. Indeed, rather than the four-goal thriller he had just witnessed, Moyes's mind was occupied by the four points that he believes he has been unfairly denied. Their finest start to a season for eight years could have been so much better but for mistakes in twin 2-2 draws, home to Newcastle and at Wigan.

After Victor Anichebe was deprived of two goals, one a header that clearly crossed the line, against Newcastle, an offside header from Arouna Koné put Wigan into the lead on Saturday. Moyes' ire was directed at the men on the touchlines. "The linesman should see it," he added. "It is up to them." Ceri Richards, three weeks ago, and Mark Scholes, on Saturday, were the errant officials and Moyes, also aggrieved that Nikica Jelavic was not awarded a penalty when fouled by Maynor Figueroa, is considering copying other clubs and confronting the referees' chief.

"We can approach Mike Riley and I am sure others do," he said. "But Mike Riley has to look at the people who are working for him and whether they are doing well enough." Wigan's normally mild-mannered manager Roberto Martínez has been uncharacteristically critical of officials of late, a tactic that Moyes feels reaped dividends. "Roberto has done a good job of making sure that the referees gave them what was required," he added.

Martínez had reverted to his usual, smiling self after the game, admiring Everton's improvement in 2012. "They are a different side," the Spaniard said. "They could easily challenge for a top-four position." And as Moyes knows, with different decisions in two games, they would still be occupying second spot and the closest challengers to Chelsea.

Man of the match Leighton Baines (Everton)