Ferdinand and Evra were booed almost every time they touched the ball at Stamford Bridge yesterday, with some drawing a link between their treatment and the race rows that have erupted in English football this season.
Ferdinand's brother Anton was the alleged victim of a racist slur from Chelsea captain John Terry, who last week pleaded not guilty to the offence ahead of an upcoming trial over the matter.
Evra, meanwhile, was racially abused by Luis Suarez back in October, something that saw the Liverpool striker banned for eight matches.
Ferdinand shrugged off the booing, tweeting: "I got booed by the cfc fans today,....well done guys thanks for inspiring me & the lads! That's like fuel to me!"
Villas-Boas said: "You don't expect opposing fans to cheer your players."
He added: "This is a normal situation in the Premier League.
"You have to condemn it when there is discriminatory, aggressive behaviour.
"We know the situations. We know we have to play a part.
"If we want to push on this sequence of events to extend in the future, it's up to us. It's up to me and it's up to you in the press.
"If you want to give importance to situations like this, if you let people take responsibility, assume responsibility and the fans and the knowledge that maybe what they were doing makes no sense, it's better but to try to prevaricate isn't right."
Villas-Boas had no such qualms when it came to his assessment of referee Howard Webb's performance in Sunday's Barclays Premier League clash.
Chelsea were 3-0 up and looking nailed on for victory when Webb awarded United two extremely controversial penalties that got them back into the game.
"The first one is an obvious penalty," said Villas-Boas.
"The second is very, very dubious. I don't know if Howard Webb had the correct angle to make the decision."
He added: "You cannot give a penalty for that."
Villas-Boas admitted on Friday he was still fuming from two offside goals United scored against Chelsea in September's reverse fixture.
He added: "We expect, in top games, top refs and, at the moment, it hasn't been happening for us.
"It didn't happen at Old Trafford with two goals offside, and maybe today a dubious decision that, in the end, shifted the running of the game."
Opposite number Sir Alex Ferguson also blasted the officials, claiming Gary Cahill should have been sent off for a last-man tackle on Danny Welbeck.
Villas-Boas said: "Sent off? I don't think so. The ball is running towards the line so the player is going nowhere.
"The foul is outside the box to be fair on that one, so maybe it was a yellow card and a free-kick."