The Chelsea boss thought that referee Howard Webb made some strange decisions that helped United come from 3-0 down to earn a point from the game.
Chelsea had a good first half and a Jonny Evans' first-half own goal was followed by goals from Juan Mata and David Luiz shortly after the restart.
But United were handed a lifeline by referee Howard Webb as two penalty decisions went their way and Wayne Rooney took full advantage with both spot kicks.
Then Javier Hernandez wrapped up the scoring when he headed home a late equaliser.
Afterwards, Villas-Boas criticised Webb.
"Of course, it's not easy to take,"he said.
"It's a massive recovery for United. We had it in our hands and let it slip.
"There were some strange decisions today though. These things just keep happening. The first one is a penalty and I agree with it. The second is very unlucky.
"I'm not sure if Howard is trying to compensate for something."