AC Milan coach Massimiliano Allegri said penalties killed his side at the Camp Nou, claiming Barcelona were gifted one by his side and one by the referee.
Lionel Messi twice scored from the spot, first after he had been fouled by Luca Antonini, then again after Alessandro Nesta was penalised for pulling Sergio Busquets' shirt.
Antonio Nocerino had made it 1-1 after he finished off Zlatan Ibrahimovic's pass, yet Messi restored Barca's lead and Andres Iniesta made the game safe with a cool finish past Christian Abbiati.
Of the second spot-kick award, Allegri told Sky Sport Italia: "It's a shame, as it was a moment of the match where Barcelona weren't doing much and it was just before the break. They had two penalties, one gifted by us, the other gifted by the referee."
Quite apart from the crucial decisions, Allegri was disappointed Milan couldn't match the quality they produced in the first leg, which finished 0-0 in the San Siro.
"We made a lot of mistakes and misplaced passes where we had the chance to run into space," he added. "We opened the game for a while and I think we go out with our heads held high.
"After it went to 1-1, we felt that we had the chance to qualify, as Barcelona had some pressure on them and it showed. It's only normal that after going 3-1 up it was all easier for them.
"It was difficult, as going into the locker room at the break with that dubious penalty, then after the restart a lucky deflection gives them a third, it gave Barcelona a psychological boost and they started to move the ball around much better.
"I think we had numerous chances to create scoring opportunities, but we misplaced many passes and got some decisions wrong. We knew Barcelona were the best team in the world right now.
"In the opening ten minutes we lost the ball too often, which is precisely what you shouldn't do against Barcelona. We often caught them one-against-one with an open field in front, but chose the wrong pass or got the measurements wrong, much like the first leg."
Milan's night went from bad to worse when Alexandre Pato had to limp off the field just 13 minutes after coming on as a second half substitute.
Allegri explained: "He felt another twinge on the back of his thigh and the medical staff will evaluate it. If he has hurt himself again, then that will be a problem, as the poor lad has been carrying these problems for two years."
Defender Massimo Ambrosini was also unhappy with the second penalty. He said: "In every level and on every corner things happen, but the interpretation changes from referee to referee. There is no uniformity.
"It takes some courage to make such an important decision in a tie like this. There are always going to be some tugs on set plays and always have been.
"We knew Barcelona are the strongest team in the world. We leave without regrets and there were differences between the teams over the two legs, but not all that much.
"It was a game where we didn't start well, then were able to fight back and it was balanced. I don't know what happened with that penalty. Barcelona played better and we didn't do enough in the second half, but we did give them a battle."