The Blues looked to be heading out in normal time after Jon Walters' 52nd minute strike, but Loic Remy scored an injury-time equaliser to take the game into a 30-minute period of extra-time.
But, with neither side able to find a winner, the game went to penalties, with Eden Hazard missing the crucial spot-kick as Stoke prevailed 5-4 in the shoot-out.
The defeat is Chelsea's eighth in 16 games in all competitions this season, but with pressure mounting over his position, Mourinho is adamant his job is safe.
Asked if he'd been given any further assurances over his job, he said: "I don't need more. My general situation is fantastic.
"I have a day off tomorrow, a fantastic family. I can sleep well every night. I'm going to enjoy my day and Thursday.
"It will be one more day like I have had in the last 15 years of my life - honest and>