Barca recorded a 2-0 semi-final first-leg win at the Bernabeu thanks to two late Lionel Messi goals after Madrid had been reduced to 10 men on the hour mark when Pepe was sent off.
Mourinho insisted his side had no chance of coming back in the second leg at the Nou Camp.
Portugal international Pepe was shown a straight red card by German referee Wolfgang Stark following a challenge on Barcelona defender Dani Alves.
In the wake of that dismissal an angry Mourinho was sent to the stands, while in an ill-tempered match Barca reserve goalkeeper Jose Pinto was also shown a red card following an incident as the teams went down the tunnel at half-time.
In the post-match press conference, the outspoken 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."
Mourinho, who is looking to become the first coach to conquer Europe with three different teams having won the Champions League with Porto and Inter Milan, also had a dig at Barca's recent success in the Champions League.
He referred back to the semi-final between Barca and Chelsea in 2009, when the Catalan club progressed through to the final following a controversial second leg at Stamford Bridge.
Andres Iniesta's injury-time strike earned Barca an away-goals win, but at the final whistle Chelsea's players confronted referee Tom Ovrebo, who had waved away at least four penalty appeals during the game.
Barca would go on to beat Manchester United in the final.
Mourinho said tonight: "Barcelona are a great team on and off the pitch, but winning like that doesn't leave the same taste.
"I have already won two Champions Leagues, and I won them on the pitch, with two teams that weren't Barcelona. I won one with Porto, a small team from a weaker league. And I won another with Inter, sweating and fighting hard.
"Josep Guardiola is a fantastic football coach, but the Champions League he won was an embarrassment because of what happened at Stamford Bridge - it was a scandal.
"And if he wins it this year, he will win after the scandal at the Bernabeu. Let's hope he gets the chance to win a clean Champions League (in future), without scandals.
"Guardiola deserves to win a Champions League normally. That's what I wish because he is a very good coach who I respect as a person for his fantastic treatment in four years with him.
"I respect him a lot as a coach and as a person, I hope that one day he will win a clean Champions League, with no incidents behind it."
Victorious Barca coach Guardiola refused to respond to questions about Mourinho's comments, or about the performance of the referee, but he did warn against assuming the tie was now over following Wednesday's result.
"We haven't made it to the final yet, this is the first leg match," he said.
"A team that has nine European Cups never gives up on a tie. We are two games and one draw from being European champions. We will think about the return so we can get to Wembley.
"We are a step away from the final, but we will carry on respecting Madrid, very, very much.
"If we start to believe we are already through, Madrid can punish us. We don't believe we are already there (Wembley)."
"We played a very good match and I would like to congratulate the team."