To add to a series of poor performances on the pitch, Mourinho has angered Real fans by dropping captain and goalkeeper Iker Casillas for the last two league matches and, not for the first time this season, they made their feelings clear by roundly whistling the Portuguese at the Bernabeu.
Casillas, a graduate of Real's youth academy who has been with the club since he was a boy, was given a rousing ovation when he came on to replace Antonio Adan after the reserve keeper was sent off in the sixth minute.
The anti-Mourinho protest and the backing for Casillas was the latest evidence that all is not well at Real and failure to get past Celta in Wednesday's last 16 second leg at the Bernabeu would leave the Champions League as the only competition they can realistically hope to win this season.
The Spanish champions are a daunting 16 points behind unbeaten leaders Barcelona after 18 of 38 matches and face Manchester United in the last 16 of Europe's elite club competition when it resumes next month.
The relegation of club hero Casillas to the bench has prompted speculation in Spanish media that Mourinho may be trying to provoke Real president Florentino Perez into sacking him so he can cash in on a lucrative payoff.
The former Chelsea manager, who has made no secret of his desire to coach in England again at some point, said after the Sociedad game he did not mind being whistled by Real's own fans as long as they got behind the team.
"This season in the [La Liga] championship, compared with last year, we are having a bad time of it and it seems normal to me to whistle and this is how I like to live," Mourinho, who turns 50 later this month, told a news conference.
"I do not like to always be in a comfortable situation or be a hero forever," he added.
"If I was whistled for the decision to leave out Iker, fine. And if I was whistled for bad performances in the league then I accept it.
"Perfect that they whistle when they hear my name and that they help the team during the match as they have done, perfect."
Real's players did show some fight in the second half against Sociedad, when Cristiano Ronaldo struck twice to put the game beyond the Basque club, and Mourinho said more of the same should see them through to the last eight of the cup.
"Celta play well, are confident, are winning 2-1, but my experience in these two and a half years is that the fans like the cup, the excitement of winning and going through," he added.
"I have a feeling that if we play with the same effort as today in two days, the team and the fans will be ready and we can go through."
Barca, the King's Cup holders, kept up their relentless pace at the top of La Liga with a 4-0 thrashing of city rivals Espanyol on Sunday and will protect a 2-0 advantage when they host second-division Cordoba on Thursday.
Coach Tito Vilanova returned to the bench on Sunday for the first time since last month's throat operation and the club have said he will alternate his work with hi
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