Theo Walcott scored the first giving the Gunners a narrow half time lead but two goals in nine second half minutes decided the tie 4-1 on aggregate to Arsenal.
The Spanish outfit's miserable night was complete when Sebastian Eguren was sent off for disputing the penalty.
Gunners skipper Cesc Fabregas felt they should have scored more goals.
He told Sky Sports, "It was important (to get the early goal). That's what we said to try to score as soon as possible and keep the pressure going. That's what we did."
Regarding the final score, he continued, "Three-nil... that is okay, we did well we could have got more but let's not be greedy. We have an important semi-final to compete in on Saturday so we will now prepare for that.
"Manchester United are the best team in Europe... in the world even. But we will just concentrate on Chelsea."
Theo Walcott added, "It was all about the team tonight."
As to the penalty, he said, "The referee gave it, so that's all there is."