The Blues suffered yet another setback in their disastrous season as they were beaten 5-4 on penalties in the fourth-round tie at the Britannia Stadium following a 1-1 draw after extra time.
Mourinho blasts rift rumours
But Mourinho was keen to praise his players' efforts and said in his post-match press conference: "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 sad for the players, and I think it is a lack of respect to the players, not to me.
"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.
"I think what some people write and say is really bad for the players. They tried everything."
Talk had already been rife before this tie about the sack looming for Mourinho, whose Premier League champions were left 15th in the table by Saturday's 2-1 loss at West Ham, in which he was sent to the stands.
Asked if he had had any more reassurances since the weekend about his job, Mourinho said: "I don't need more."