Villas-Boas was angered by the manner of his first defeat as manager of Chelsea, which was also his first reverse in a league game for 17 months.
Chelsea went 2-0 behind at Old Trafford on Sunday to goals which replays showed should not have stood as both scorers had been offside, with United finishing 3-1 winners.
Villas-Boas said: "[I am] very, very unhappy with a poor performance from the referees, which in the end had a decisive role in the result, and I don't take it very, very lightly. You expect the linesman to do his job.
"I already went further ahead with the situation by speaking to the correct people. We all feel very, very down when the referee had such an impact on the result."
Chelsea were also let down by their own wastefulness in front of goal, with Fernando Torres producing one of the worst misses in Premier League history. Villas-Boas refused to comment on his £50m striker's state of mind, saying: "It's not a question about an individual player. I'm very, very happy with how the team responded. Everybody is strong and with the correct frame of mind."
However, the Chelsea manager suggested Torres would have to wait for the chance to redeem himself, revealing he planned to pack his team with youngsters for Wednesday's Carling Cup third-round tie with Fulham.
"It gives us a very good idea of where we stand regarding the young players that we are trying to bring through," said Villas-Boas, who announced that Josh McEachran, Romelu Lukaku, Oriol Romeu and Ryan Bertrand will all start. Didier Drogba will lead the line after recovering from his head injury.
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