Barca took a 2-1 first-leg lead into Wednesday evening's game at the Nou Camp, and seemed to be cruising to a semi-final berth after taking a 2-0 lead through Pedro Rodriguez and Dani Alves.
However, Cristiano Ronaldo and Karim Benzema hit back for Real, but they were unable to find a vital third goal that would have seen them go through on away goals.
But despite their failure to successfully defend the title they won last season, Mourinho insists there are plenty of positives that can be taken from the match.
"It was easy to talk to my men during half-time," Mourinho said on the club's official website. "I had few things to change.
"Half-times are short when your team isn't playing well; those ten minutes don't seem enough.
"I only needed one minute today [Wednesday] because my team played very well in the first half. I told them to keep it up."
However, one aspect of Real's performance Mourinho was slightly disheartened by was their inability to hurt Barca on the scoreboard despite carving out a plethora of chances.
"You sometimes score a goal without trying much for one and we happened to fail to score from four or five of our chances.
"We looked for more depth in attack through Karim and [Jose] Callejon, with Cristiano Ronaldo playing inside."
Real also had Sergio Ramos sent off towards the end of the game for a second bookable offence, and Mourinho hinted that he was not too pleased with some of Barca's tactics throughout the match.
"Maybe [Barcelona coach] Pep Guardiola congratulated us after winning last year's final because it was a clean match without any havoc," Mourinho added.
"If you like, I'll congratulate him for winning last week's match. I have no problem doing so.
"They deserved to win that game."
Midfielder Xabi Alonso added that despite going out, Real had at least restored their pride in the second leg.
"We have come very close," Alonso said. "This team has qualities and potential."
"Today [Wednesday] we played a great game, we had chances and [Barca goalkeeper Jose Manuel] Pinto played very well. We don't leave here happy but we are proud."
Real will be looking to bounce back when they take on Real Zaragoza in La Liga on Saturday.