The Scot was certain the Belgian defender deserved to be dismissed for a 'two-footed' challenge but couldn't hide his disappointment at his side's 'careless' second-half display
Kompany was dismissed by referee Chris Foy for a challenge on Nani that Sir Alex labelled as "two-footed" and argued that the Portuguese winger could have been seriously hurt had Kompany made more contact.
"It was a two-footed tackle," he told ITV.
"I think it was a red card, absolutely - I’ve seen him do it before.
"Maybe he’s got off with it in the past, but we’re lucky because if he makes contact with Nani, he’s got a problem.
"It would have been a real bad one. I think the referee was right in that instance."
Despite his side's progression to the fourth round of the FA Cup, Sir Alex was critical of a "careless" second half performance that gave City a way back into the match, with United having raced into a 3-0 lead.
"I think we made them better than they were with our carelessness in the second half," he said.
"I think the problem was, at 3-0 up at half-time, we thought we were through. We took our foot off the pedal, lost possession just after half time, gave away the free-kick and they scored.
"They went into a defensive formation which you have to give them full credit for. They just waited and waited for us to make mistakes and we were making mistakes.
"They made it a score line it shouldn’t have been. There were three phases, I think.
"First we scored a goal, which was terrific, we were going to be very difficult to beat at that point.
"Then the sending off, obviously. The third phase was at 3-0 – we should have been home and dry, but no, we made mistakes and you suffer if you make mistakes."
Sir Alex added that despite the win, the nature of his side's performance meant that it would not do them any good in terms of gaining an edge in the Premier League title race.
"I don’t think it does us any good at all today," he said.
"It was a careless performance in the second half.
"We should have been home and dry. We were too careless in the second half and, if we keep doing that, we’re going to make mistakes."