Rafael was shown a straight red card late on by Howard Webb after lashing out at Luiz near the corner flag as United chased an equalizer.
Luiz appeared to rile his fellow Brazilian in the seconds leading up to the incident by forcefully shielding the ball, and was caught on camera smiling as he lay on the floor after being kicked.
"It was the elbows," Sir Alex told Sky Sports after the match. "He retaliated. That’s always happened. The player that retaliates always gets the bigger penalty. It was quite clear that Luiz has elbowed him, twice actually, and it’s rash what he’s doing. He’s a young lad and he should know better that retaliation never works.
"I wouldn’t say it was violent conduct. The referee hasn’t even seen it, I don’t think he can see it at all. But he’s gone with the fact that Luiz has rolled about on the floor and I think that’s convinced him it’s a red card."
The United boss also criticized the performance of Webb and the actions of Chelsea players during the match, though he conceded the Blues were worthy winners.
"We weren’t getting anything from the referee," he added. "It was a bit of a lucky goal – it’s deflected off of Phil Jones – so we had bad luck for that but I can’t make any excuses for my players in terms of our performance. Certainly the referees’ decisions went against us I thought. They surrounded the referee all day, four and five players all the time. I think that affected the referee.
"We’ve taken our foot off the pedal in a big way and there was no real edge to our game all day and I think Chelsea have deserved to win. Unfortunately it’s controversial, it sometimes is when you play Chelsea, quite a lot of times. But we can’t complain, we didn’t play well enough."