The club has been forced to dismiss reports claiming that Mourinho is set to lose his job at Old Trafford and Rooney believes the Portuguese has been made a scapegoat for the club's underperforming players.
The second half saw the French midfielder play one of his best matches of the season, before Alexis Sanchez claimed a dramatic late victor. Some of the players have to be better.
The former England forward said the situation at Old Trafford was similar to when Louis van Gaal was at the helm.
"I know Jose is getting a load of stick but I said a few weeks ago, the players have to stand up".
Rooney - who left United past year as the club's all-time record goalscorer - now plays for DC United in the MLS.
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"I have begun to feel that if it rains in London tomorrow it is my fault", he said.
However, after some peculiar substitutions and a half-time break, the Red Devils mounted an extraordinary comeback reminiscent of their exploits in the late 90s under Sir Alex Ferguson, to win the game 3-2.
Woodward will be mulling over those figures, particularly as the compensation would drop to just £10m if he stays in place until the end of the season and United don't qualify for the Champions League. In my eyes, they are the best team ever and Messi is the best player ever.
"I've been sacked twice and it hurts when people level things at you, in defeat or at bad times, it can get personal and maybe some of it has got personal with Jose".
Pressure had built on Mourinho throughout an inconsistent opening to the campaign, but he can breathe a little easier after overseeing a stirring fight back from two goals down against the Magpies.