But Liverpool boss Kenny Dalglish insisted it was "bang out of order" to only blame the 25-year-old.
Hansen and Shearer on Suarez
Here's a round-up of what players and pundits have been saying about the controversy:
Manchester United defender Rio Ferdinand,
who refused to shake Suarez's hand after the Liverpool player snubbed Evra, told MUTV: "After seeing what happened, I decided not to shake his hand. I lost all respect for the guy.
"He has not got the respect that he needs to acknowledge he's made a mistake and say sorry and move on from that. It could have been resolved between the two players today. After this, it's not great."
Former Liverpool defender Alan Hansen said on the BBC's Match of the Day:
"The rhetoric from both clubs before the game was restraint. Liverpool said there would be a handshake, so for Suarez to snub Evra is totally unacceptable. Liverpool have given Suarez total support through thick and thin and I think he's let Kenny down, he's let the club down and he's let himself down."
Former Newcastle and England striker Alan Shearer told the BBC's Match of the Day:
"Kenny [Dalglish] is fiercely loyal but Suarez has let him down. This should have been the start of the end. I totally disagree with Suarez not shaking his hand. Evra puts his hand out - and then Ferdinand chooses not to shake [Suarez's hand]. It's not a great day for football." On Evra's post-match celebration, he added: "There was no need for Evra to do that in front of Suarez, who keeps calm."
Former Liverpool striker John Barnes said on ESPN:
"When I saw it live and they didn't shake hands, it just amazed me. I can't imagine after everything that has gone on this week that this was not discussed by Liverpool in terms of are they going to shake hands or not.
Phil McNultyChief football writer, BBC Sport
"If the intention was to draw a line under this affair, Suarez's actions torpedoed it and Liverpool were once again left to deal with the fall-out. How will Liverpool's American owners - still silent on the other side of the Atlantic - feel about Suarez once again acting in a manner that has caused their club to be portrayed in an unflattering light?"
"It's a big shock and was compounded by Evra at the end [celebrating near Suarez] and then Sir Alex Ferguson. It's not a good day from a PR perspective for either club."
However, Barnes also insisted too much had been made of the whole row between the players, adding: "For me, we are making a mountain out of a molehill. There are worse things happening in the world."
also played down the handshake snub, insisting: "I haven't seen it. A few of the lads were talking about it but we've got to just focus on the game. It's between the two of them, it's nothing to do with us. We had to just focus 100% on the game and make sure we got three points."
Former England manager and Liverpool striker Kevin Keegan
was unimpressed by Ferguson's call for Liverpool to sell Suarez, insisting both clubs have behaved badly over the issue: "To come out and say a player shouldn't play for another club that you have no control of, I think is wrong. Instead of calming this down, they've allowed it to escalate.
"They are the two biggest clubs in this country in terms of winning things and I think both clubs at different times have handled it badly, I think Liverpool in the beginning very badly.
"Today was a chance to say to the player, 'Shake his hand and get on with it', and then there's nothing to say. Then Evra after the game, why would he want to do that? He's won his case, the guy's got a lengthy ban, just keep quiet. You've won the game."
Tensions run high as Evra celebrates victory
former Tottenham and Stoke striker Garth Crooks, speaking on the BBC's Final Score,
said he felt the blame lies with Liverpool, saying: "This has left a sour taste. Liverpool have had numerous opportunities to draw a line under this. Today was an opportunity to do it and they blew it.
"It's a real shame. I don't accept Kenny Dalglish saying he does not want to talk about it. What does that mean? Does he agree with it?"
BBC pundit Steve Claridge told Final Score:
"I'm with Sir Alex here. It was a poor way to behave and he [Suarez] has made himself out to be a villain.
"To shake someone's hand before a game is to wipe the slate clean. To not do that is not acceptable behaviour."
Former Liverpool defender John Scales told BBC Radio 5 live:
"It's incredibly disappointing. We all expected a handshake - Sir Alex Ferguson did, Kenny Dalglish did - and it took everyone by shock."
However, Scales also insisted that Evra's behaviour helped to inflame the situation. "There are certain players who have real control of their emotions and I think Patrice Evra is quite a volatile character. That celebration at the end of the game was overdone," he added.
Former Football Association chief executive Mark Palios told BBC Radio 5 live's Sportsweek
that the handshake was "clearly symbolic, and its symbolism has its place in the game.
"From a player's perspective it's very difficult to shake someone's hand if you don't want to.
"But players have a responsibility to their club and to the wider interests of the game. If it can cause more problems in a particular circumstance, it's right for the clubs to dispense with it.
"You cannot have two of England's most famous and proud clubs at each other's throats on an instance like this, and I think they [the FA] will have to bring the two clubs together - it cannot carry on like this."
Former Arsenal and FA vice-chairman David Dein told BBC Radio 5 live's Sportsweek:
"Handshakes should be respected. Football first and foremost is a sport and sporting conduct has to be encouraged. What happened was unfortunate and an embarrassment.
"All clubs sign up to Fifa's and Uefa's Fair Play and anti-racism campaigns and they have got to be respected. Players have to respect that, they are role models to youngsters."
Former Liverpool manager Gerard Houllier told BBC Radio 5 live's Sportsweek:
"I regret what happened because it would have been a good opportunity to put everything to bed.
"It created some tension, I was at the game and I could feel it, the atmosphere was a bit toxic but at the same time I am a bit disappointed because it overshadowed the quality of the game.
"It was a good game of football between two good sides but instead we are talking about what Suarez did or didn't do."
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