When finally it did come yesterday, the apology from Luis Suarez was not directed to Patrice Evra in person but was offered rather more for the manner in which his actions before the match at Old Trafford on Saturday had reflected poorly on Liverpool.

As for those apologies that came from Kenny Dalglish and Ian Ayre, the club's managing director, they too were angled to reflect their disapproval of Suarez's failure to shake Evra's hand and the repercussions that it had for the reputation of the club. Ayre said Suarez's behaviour was "not acceptable" and that he had "misled" the club and "let down" Dalglish.

Dalglish said he was "shocked" when he learnt that Suarez had not shaken hands with Evra at the start of the game and he apologised for the manner in which he behaved in his interview at the end of the match which, he said, was not "befitting of a Liverpool manager".

Given the events of the weekend and the potential damage that this latest instalment between these two clubs could have done had it been allowed to linger on through the week, this move from Liverpool was a welcome concession. That Manchester United accepted the apology is the best test of its value and confirmation that it has defused the immediate potential for chaos.

English football in general will breathe a sigh of relief that, in this instance at least, the tricky issue of race can be put to one side and managers, players and even pundits will no longer have to pick their way through the minefield. But the Suarez-Evra case leaves inevitable scars on the game that will be a little less easy to heal.

What has not been changed by yesterday's apology is the fact that Liverpool still ultimately reject the ruling by the independent regulatory commission on New Year's Eve that Suarez was guilty, as charged by the Football Association, of racially abusing Evra. The Liverpool striker may have served his punishment for doing so but as recently as one week ago Dalglish said in a television interview that the player "should never have been banned".

That is the basic contention that remains unchanged by Liverpool, however much Fenway Sports Group and the principal owner, John W Henry, might have leaned upon the club to apologise yesterday. When the club waived the right to appeal Suarez's case last month it continued to argue that the FA's case was "highly subjective" and "ultimately unsubstantiated".

For those of us who still find it bewildering that Liverpool have rejected out of hand a 115-page ruling from one of the country's leading QCs, drawn up in accordance with the rules that all clubs endorse, there is still some way to travel down the road to redemption. Yesterday's apology was a step in the right direction but it addresses only Saturday's developments, not the four months that followed the original game on 15 October.

Unfortunately, those battle lines are still drawn and while there remains a wholehearted rejection of the regulatory commission's ruling on Suarez by Liverpool so there remains considerable doubt. And while there is considerable doubt there is the potential for bad feeling between these two teams on a level that is unprecedented in the game.

On Sky Sports on Saturday, Gary Neville compared the bitterness between the two players in question to the great rivalries that existed between Arsenal and United in the previous decade. It was a good deal more serious than that. Martin Keown v Ruud Van Nistelrooy was nasty at times; Patrick Vieira and Roy Keane once clashed over Vieira's international allegiances, but they were not based on racial slurs.

There are times when football – English football, that is – just does not seem to know how to react to the issue of race. When no less than John Barnes says, as he did on ESPN on Saturday night, that we were in danger of making "a mountain out of a molehill" on the Suarez issue it is necessary to fight the urge to go into an empty room and scream.

As for Dalglish, he was caught out when questioned about Suarez on Saturday by Geoff Shreeves on Sky Sports, and reverted to the way he knows best: an immediate and unqualified backing of his player. He does not have to do that and if the episode has taught him anything it is that the old managerial maxim about keeping all criticism in-house no longer applies.

No manager can hope that his club will be on the side of right all the time. All football clubs are such disparate entities, full of all sorts of crazies, that most players let the manager down at some point. He sacrifices credibility by defending them. Sir Alex Ferguson has not always abided by that rule but he did so on Saturday when he acknowledged that Evra should not have provoked Suarez at the end of the game.

The Suarez saga cannot take responsibility for other outrages committed along racial lines in the game but as an episode it has been allowed to go dangerously open-ended for so long. That is not helpful in a charged atmosphere where Micah Richards has closed down his Twitter account because of racist abuse, presumably the same kind that Stan Collymore retweets regularly.

The Suarez-Evra row is not another great chapter in the rich history of the English game. It is not another compelling rivalry. Quite frankly, it has been an embarrassment, which Liverpool, and Dalglish, have at last gone some way to addressing. Yesterday's apology was certainly a start.