“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.”
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 a consolation in the 80th minute.
It was the first time the two sides have met since Suarez completed his suspension.
And, 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.”
Ferguson, however, had a different point of view and believes the racism issue is one which needs to be addressed.
“I couldn’t believe Suarez refused Evra’s handshake,” he said. “You saw the referee [Phil Dowd]. He didn’t know what to do. It was a terrible start to the game and it created a terrible atmosphere.
“Racism is an important issue and football has come a long way since the days of bananas being thrown at John Barnes.”
The United boss believes Evra “kept his dignity” by offering to shake Suarez’s hand, but did not condone the Frenchman’s post-match celebrations.
“Evra shouldn’t have jumped in front of Suarez in celebration at the end,” he added. “He shouldn’t have done that.”
United players Rio Ferdinand and Darren Fletcher, who is still on the sidelines with a chronic inflammatory bowel condition, were also quick to condemn Suarez’s actions, while supporting their team-mate.
“After seeing what happened, I decided not to shake his hand … I lost all respect for the guy,” Ferdinand said.
“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.”
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”.