The game, and the tie, was tied at one goal apiece, with Antonio Nocerino having cancelled out Lionel Messi's opening penalty, when Kuipers deemed Alessandro Nesta guilty of a tug on either Sergio Busquets or Carles Puyol as the trio jostled in the area shortly before the break.
Milan were enraged by the decision but Alves felt that the official had made the right call.
"The majority of referees don't have the personality they need [at this level]," the Brazil international told reporters after the game. "If it's a tug in the area, then it should be given. So the referee showed character.
"But I am happiest above all with the great work of the team, which helped us fulfil our objective.
"We wanted to fight to be in the next round because as you get closer to the final it gets harder and more difficult. We knew we couldn't commit any errors and we had to be very attentive."
Meanwhile, Javier Mascherano refused to dwell on the controversy surrounding Barca's second spot-kick, arguing that the right team had gone through at the end of the day.
"They had practically no scoring chances, and that is down to the defensive work carried out by the whole team - not just the defence," the Argentine midfielder argued.
"Now let's hope we can be in a third final in four years. It would be great for the club but there's still one more step and it will be just as hard - or even harder."
Barcelona will now face the winners of the quarter-final tie between Chelsea and Benfica in the last four.
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