The Blues suffered yet another low in their disastrous season on Tuesday as their defence of the cup was ended with a 5-4 loss on penalties following a 1-1 draw after extra time.
But their embattled boss Mourinho was keen to praise his players' efforts in the fourth-round tie afterwards and hit back at any suggestion they are not behind him, saying: "What I think they did was face some people who have written and spoken (about them) and said 'you are stupid'.
"Honestly, do you think they are not with me? That they didn't give everything to win the game?
"That is really sad - not sad for me but for the players, and I think it is a lack of respect to them.
"For me, it would be a fantastic situation if the players are against me - I could say we don't have results because the players are against me."
Talk had already been rife pre-match about the sack looming for Mourinho, with the sense of crisis around Chelsea having deepened after Saturday's trip to West Ham ended in another damaging Premier League defeat and saw the Portuguese - subsequently hit once again by a misconduct charge from the Football Association - sent to the stands.
But, speaking publicly for the first time since then, Mourinho did his best after the Stoke game to appear relaxed about his future, saying: "My general situation is fantastic
I can sleep well every night."
Asked if he had had any more reassurances since the weekend about his job, Mourinho said: "I don't need more.''
Chelsea played well in the first half despite the loss of striker Diego Costa, who Mourinho said had come off due to a rib injury and gone to hospital.
But, having failed to make a breakthrough, they fell behind in the 52nd minute when Jonathan Walters cracked in a superb effort.
Substitute Loic Remy - on for Costa - then dramatically levelled in the first minute of time added on, and moments later Stoke had Phil Bardsley sent off.
The visitors were unable to make the most of their man advantage in extra time, though, and their exit was subsequently sealed when Eden Hazard's spot-kick, the 10th of the shoot-out, was saved by Jack Butland, who had been on fine form throughout the game.
Stoke boss Mark Hughes said: "He made any number of saves.
"Chelsea were probably the better team in the first half - in the second I think we edged it, with Jonathan Walters scoring a fantastic goal.
"I thought we had done enough in normal time to take the game away from them, and then there was great drama at the end
I'm just glad it has gone our way.''
Source : PA