His rivalries with Guardiola - whose side, now eight points clear of United at the top of the Premier League, United play at Old Trafford on December 10 - and Gunners boss Arsene Wenger are both well documented. The United resistance prompted the Frenchman to state De Gea was "man of the match by a clear mile".
After the break he continued to thwart Arsenal's best efforts, making an astonishing double save to first keep out Alexandre Lacazette's shot, then stuck out his leg to deny Alexis Sanchez from point-blank range.
Only Tim Krul - for Newcastle against Tottenham in 2013 - and Vito Mannone - for Sunderland at Chelsea in 2014 - have recorded 14 saves in a game since Opta began gathering this piece of data in 2003-04.
"I loved the way my team played and fought", Mourinho said.
"We started with that desire and intensity, we played high and created mistakes", he said.
"I'm just disappointed and angry that with the quality of that performance we have nothing to show for it", he said, attributing his team's loss to a lack of efficiency in finishing and De Gea's "outstanding game".
There was much to admire in Arsenal's attacking play but they never fully recovered after defensive sloppiness allowed Antonio Valencia and Jesse Lingard to put a livewire United side 2-0 up after 11 minutes.
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Danny Welbeck and Alexandre Lacazette, appealed in vain for penalties and, with his tongue firmly in his cheek, Mourinho said: "I know the pitch is incredible and maybe breeds a desire to go to the floor".
"But I have to say that my players deserve all the great words - I don't know so many more in English".
Twitter reacts as Manchester United manage to steal away three points from the more dominant Arsenal, who will be kicking themselves after not being able to capitalise on some serious pressure from start to finish.
They comfortably held on despite Paul Pogba being sent off for a unsafe challenge late on, punishing Arsenal for early defensive mistakes.
"It was a big blow to go 2-0 so early on - especially at home. But when you go into a big game, you can not make the mistakes that we made". The attitude was impeccable until the end.
"You can not give any other message out".