Victory left United five points adrift of Premier League leaders Manchester City, ahead of next week's Manchester derby.
"You need the keeper to be there for you when the team needs", the Portuguese boss added.
"I don't believe in that s***", he said bluntly.
And the nature of United's vibrant display answered the critics who have accused Mourinho of "parking the bus" in away games against the sides challenging for top-four places.
"He was a doubt, he managed to play 90 minutes but I think the best words must go to Arsenal's medical department because [Alexandre] Lacazette went from a "no" to a "90 minutes" and that's great". But I have to also say that Arsenal played, in some periods, amazing, attacking football, creating difficulties for us. "I leave for you the Lukaku situation with Koscielny, I leave for you the Arsenal players on the grass". I don't know so many more in English! He brilliantly denied Alexis Sanchez at point blank range as United secured all three points at the Emirates.
Once again Jose Mourinho took the best of Wenger's coaching and Arsenal. We were going at 2-1 with 25 minutes to go and could come back, but the 3-1 is the killer.
As impressive as those shot attempts and expected goals stats are, the biggest reason why the game's score did not match the underlying statistics was de Gea, who faced down all 33 of those shots-16 of which were on target-and was equal to almost all of them.
"There are not many times you play United and you dominate the whole game, having so many chances, so this is positive, but we are disappointed". The attitude was impeccable until the end.