Action must be taken to ensure there is no repeat of the controversies that have tarnished English football this season, Brian Barwick has told the BBC.
Luis Suarez's refusal to shake hands with Patrice Evra on Sunday was the latest in a series of incidents that have overshadowed the actual sport.
"You've got to make sure some of these things don't happen again," said former Football Association boss Barwick.
"This stuff is against everything the game stands for and is not welcome."
Suarez declined to offer Evra his hand as the teams lined up before the match, while the United skipper added to tensions at the final whistle when he celebrated in front of the Liverpool striker.
It was the first meeting between the pair since Suarez served his eight-match ban for racially abusing Evra at Anfield in October.
In a separate case, Chelsea skipper John Terry is accused of racially abusing QPR's Anton Ferdinand.
Another issue to have dominated the game is Carlos Tevez's dispute with Manchester City, which dates back to 28 September.
But Barwick feels it is now time to concentrate solely on matters on the pitch.
"The football being played is terrific, the status of the game all over the world is terrific," he told BBC Sport. "Let's make sure it's not spoiled by individual incidents.
"We've got to get to the end of the season, reflect on it as a whole and make sure the right messages get to the right people.
"You need to let this roll through, take a breather, have a look at it and see if there's anything you need to do moving forward."
Former Liverpool defender Gary Gillespie admitted that his club's reputation had been damaged by Saturday's events but called for a line to be drawn.
"It can be repaired," said Gillespie of Liverpool's global image.
"Liverpool are an institution, as are Manchester United, and we want to get back to talking about football.
"These two football clubs are the most successful in British history. That's what we've got to take, look forward to the future and not dwell too much on the past."
Gillespie's views were echoed by ex-Manchester United left-back Arthur Albiston, who admitted that Saturday's spectacle was "a sad reflection on English football".
"Liverpool and Manchester United are the best-known English teams throughout the world," he said. "And that's the sad thing. This game was going worldwide, not just in Britain.
"But we've got to move on. Liverpool, Kenny Dalglish and Suarez have been big enough to come out and apologise, so let's get back to positive things.
"Hopefully when they play next season it will be handshakes all round."