"Suarez is a disgrace to Liverpool Football Club," said United manager Ferguson. "He should not be allowed to play for Liverpool again. He could have caused a riot."
Liverpool manager Kenny Dalglish said in an interview: "I think you're bang out of order to blame Luis Suarez for anything that happened here today."
Tensions run high as Evra celebrates victory
As well as the handshake controversy, the two sets of players reportedly clashed in the tunnel at half-time before Liverpool players reacted angrily to Evra's celebrations at the full-time whistle.
Wayne Rooney scored twice early in the second half before Suarez, who was
banned for eight matches
after racially abusing Evra when the sides met in October, netted an 80th-minute consolation.
It was the first time the sides have met since Suarez completed his suspension.
In a post on Twitter,
the striker said: "We lost and we are sad because we have made a big effort... Disappointed because everything is not that it seems..."
Dalglish, who did not attend his traditional post-match press conference with the written media, told Sky Sports he did not see Suarez refuse to shake hands with Evra and does not blame the Uruguayan for the bad blood that marred the contest.
"I never knew Suarez refused to shake Evra's hand," Dalglish said. "I wasn't there, I never saw it. It's contrary to what I've been told."
As is customary for him, Ferguson did not attend a post-match press conference either but told television interviewers he had a different point of view and believes the racism issue is one which needs to be addressed.
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?"
"After seeing what happened, I decided not to shake his hand ... I lost all respect for the guy," Ferdinand
"It could have been resolved between the two players today. After this, it's not great."
Fletcher added: "Credit to Patrice Evra, I think he's come out (and) he's the bigger man."
BBC pundits were also critical of Suarez.
Liverpool should 'get rid of' Suarez - Ferguson
"I'm with Sir Alex, here. It was a poor way to behave and he's made himself out to be a villain," said Steve Claridge, who played more than 1,000 professional matches during his career.
"To shake someone's hand before a game is to wipe the slate clean. To not do that is not acceptable behaviour,"
Former Stoke and Tottenham striker Garth Crooks added: "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?"
Before the game, thousands of copies of a Manchester United fanzine, which featured a "potentially offensive image",
were seized by police.
The Red Issue fanzine featured a cut-out Ku Klux Klan-style mask with the words "LFC Suarez is innocent".
The focus on the pre-match handshake, which is part of the Football Association's 'Respect' campaign, was just as intense a fortnight ago in an FA Cup match between Chelsea and Queens Park Rangers.
QPR defender Anton Ferdinand - the younger brother of Rio - was spared having to decide whether to shake the hand of John Terry when the FA allowed the teams to forego the ritual.
That match was the first meeting of the west London rivals since Terry was alleged to have racially abused Ferdinand during a Premier League match in October.
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