Stoke goalkeeper Jack Butland pulled off a stunning save to palm away Eden Hazard's penalty and seal a 5-4 shootout win for the Potters, handing Mourinho his eighth defeat in 16 games this season.
The disastrous run of results has already prompted the club's hierarchy to issue a public statement backing the manager, and Mourinho insisted he did not fear for his job.
"I don't need it (reassurances), I don't need more. My general situation is fantastic," the 52-year-old told reporters after the game.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"I have a day off on Wednesday, fantastic family, I can sleep well every night. And Thursday will be one more day like I have in the last 15 years of my life."
The Portuguese, who has seen speculation over his future build in recent weeks with each new setback on the pitch, lashed out at suggestions that his players were not behind him.
"Do you think the players are not with me or didn't give everything to win the game? It's sad for the players. It's a lack of respect to the players, not to me," he said.
"For me it would be a fantastic situation if the players were against me, (because) I could say we didn't have the results because the players were against me."
Mourinho said the performance had answered Chelsea's doubters and slammed the media for their criticism.
"We played very well," he said. "What the players did tonight was face some people who have written and spoken (about them) and said: 'you are stupid'.
"I think what some people write and say is really bad for the players, and because most that do that were players, maybe they think my players are like them when they were players.
"My players don't do that."
Striker Diego Costa picked up an injury during the game that could rule him out for Saturday's Premier League clash with Liverpool.
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
