Mourinho and Pepe were both sent off before Lionel Messi struck twice for the hosts.
Mourinho hit out at the referee and admitted his side's chances of getting to next month's final at Wembley had been crushed.
"Yes, we are out. Sometimes I am a little bit disgusted to live in this world, but this is the world we live in," he said.
"We will have to go to Barcelona and look for some pride, without Pepe who didn't do anything, without (Sergio) Ramos who didn't do anything and without a coach to sit on the bench."
Ramos also picked up a booking which will mean he is suspended for next week's second leg at the Nou Camp.
"As soon as Pepe was sent off, all of their problems were solved," continued Mourinho, whose side have had a player sent off in all four meetings with Barca this season.
"If, in a sporting sense, it's difficult to turn this around, I would say it's now mission impossible.
"If we go there (Nou Camp) and score a goal, they will kill us again. We have no chance.
"They have to get to the final and that's that."
Mourinho's rant lasted for more than five minutes at the start of his post-match press conference.
On the subject of his own dismissal, he added: "I said nothing to the referee. I just laughed and applauded his decision without saying anything.
"I'd rather say no more because if I tell him and UEFA what I really think my career would end here and now. Since I cannot say it, I'll ask a question: Why?
"We are talking about a fantastic team (Barcelona) but I don't understand how the referee, in an even game like today, could do what he has done.
"The referees are there to assure equality for everyone. Then, may the best team win."