Arsenal forward Theo Walcott came out after the game and said they had sent out a message that they are going to have a real go at winning the Premier League.
But Walcott also said the performance was for the fans after what happened at Emirates Stadium in Tuesday's Champions League defeat by Olympiakos.
That illustrates Arsenal's problem. We saw a reaction against United but, to be honest, it came five days too late.
I was expecting that kind of display against Olympiakos after Arsenal were beaten by Dinamo Zagreb in their opening game in Europe and I was amazed we did not get it.
Instead, they were poor against the Greek side. It should not have taken another defeat to bring that sort of reaction from the players.
This performance and result should be a real springboard for them, as well as a huge confidence boost going into the international break, but I would have my doubts whether it will be because they have been so inconsistent in the past.
Part of that is their own doing. As I said on Match of the Day 2, they should always pick their best available team, and that means picking their best goalkeeper.
They did that on Sunday and, although Petr Cech only really had one save to make in the first half, it was a vital one.
Cech made a brilliant stop from Anthony Martial which meant the Gunners went in at half-time 3-0 up, not 3-1. The second half would have been a different story if that had gone in.