Manchester United boss Sir Alex Ferguson made his views on Carroll's challenge plain and suggested the officials' decision-making had not helped his team.
Asked for his opinion on the incident that sent De Gea tumbling to the floor, he told Sky Sports 2: ``I think it's obvious, I don't think we need to dwell on that, it's an obvious red card but the referee has seen it differently.
``We know how they play, the ball is in the air most of the time. You've got to defend those things and they're very, very aggressive so you hope there's a strong referee. I'm not so sure we got that tonight.''
Despite those misgivings, Ferguson was proud of his players' resolve and declared it the performance of ``champions''.
United are 13 points clear of rivals Manchester City, who have six games to play to the Red Devils' five.
``We had to stand up to a lot, we went down twice but we kept going. We played like champions tonight,'' he said.
``It was magnificent in terms of determination and courage to play.
``It's one more game away...that's five left - three at home and three away. We're determined to win, we don't like losing and they showed that tonight again.''