United were held by Arsenal after Olivier Giroud's late header stunned Old Trafford.
Arsenal were shocking all day but the France international saved Arsene Wenger's blushes.
And Mourinho has praised United fans, claiming they reacted in the right way.
"I think we have amazing fans – the way they react after this draw is amazing, because they know the players did fantastic work," Mourinho told MUTV.
"They can control their disappointment with the result to praise the players and their performance."
The 1-1 draw leaves United in sixth spot and Arsenal in third.
