But while many in the footballing world have condemned the former Atletico Madrid man for his part in getting Gunners defender Gabriel dismissed, as well as seeming to raise his hands to Laurent Koscielny, the Portuguese had an entirely different opinion, labelling him the game's best player.
"To win these matches you need stability and emotional control," Mourinho told BBC Sport.
"For me he [Costa] was man of the match for sure, he brought everything to the game, he played the game like a game like this has to be played."
Mourinho's comments are sure to incite Arsenal fans even more after the Gunners felt the Spanish international was lucky to still be on the pitch following a series of clashes with the defenders tasked with stopping his aggressive attacking game, and the ex Real Madrid manager didn't relent in his post match press conference.
Unsurprisingly, it was precisely the opposite of Arsene Wenger's reaction to the forward's performance, with the Frenchman labelling it "disgusting" in his own post-match interview with the BBC.
The appreciation of Costa may be generally confined to the realm of Chelsea fans, but however infuriating his performances are for opponents, and there is no denying that he pushes disciplinary boundaries consistently in matches, that is of course something that has long been involved in football, with both defenders and forwards trying to tempt the other team's players into a reaction when the referee isn't looking.
Costa may be better at that than other players, but referee Mike Dean certainly failed to manage the situation as it developed, while the Chelsea boss was right that his attacker was a game changer, even if he could have been dismissed for the way he went about it.