Suarez deliberately withdrew his hand when he came face to face with United captain Evra for the first time since being given an eight-match suspension for racially abusing the French defender during a Premier League encounter at Anfield in October.
The Uruguayan's behaviour infuriated Ferdinand, who then snubbed Suarez's attempt to shake his hand during the traditional pre-match greeting.
The incident came two weeks after the Football Association scrapped the handshake prior to Chelsea's FA Cup fourth round tie at QPR and an equally tricky reunion between Rio's brother, Anton Ferdinand, and John Terry, who has been accused of racially abusing the defender last year.
"I thought it was bad decision-making from their guy," Ferdinand told MUTV.
"It's a touchy subject at the minute and things could have been put to bed a little bit easier if the handshake had been done.
"After seeing what I saw I decided not to shake his hand.
"He's not got the respect that he needs to have in these situations and acknowledge he's made a mistake and say sorry and move on from that. I lost all respect for the guy after that.
"It could have been resolved, maybe, between the two people who are involved.
"It's disappointing. I expected more from the other guy but it wasn't to be."
Ferdinand is not the only high-profile figure to blast Suarez in the aftermath of United's explosive 2-1 win, which also reportedly featured a tunnel confrontation between Evra and Suarez.
United boss Sir Alex Ferguson called Suarez a disgrace before claiming Liverpool should sell him, while Gordon Taylor, chief executive of the Professional Footballers Association, has branded the Uruguayan's conduct as "disrespectful, inappropriate and embarrassing".
Taylor, who has worked tirelessly to stamp out racism within the game, believes the Football Association should take more action to avoid any further incidents.
"What Suarez did was disrespectful, inappropriate and embarrassing," he said.
"If anything, Patrice Evra was the victim and he was prepared to put his hand out.
"These players are expected to be role models but if we have a situation where nobody accepts the findings of hearings and just carries on regardless, all you get is anarchy.
"Now the Football Association have to step in because the whole situation has gone too far.
"Suarez had a chance to put everything to be yesterday, in front of a worldwide audience.
"The fact that he chose not to is, quite frankly, depressing."
Meanwhile, British prime minister David Cameron is reportedly expected to step into the row over racism in football by staging a Downing Street summit.
Cameron and culture secretary Jeremy Hunt are to hold a "round table discussion" with the sport's authorities and players' representatives later this month, according to the Sunday Telegraph.
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