Lionel Messi netted a penalty after 11 minutes, scored with a second spot-kick just before the break and then helped to set up Barca's third goal for Andres Iniesta as the Catalan side ran out 3-1 winners at the Nou Camp.
But Ibrahimovic, who had been touted as the main threat to Barca's progress after a goalless draw in the first leg at the San Siro, was left ranting about the referee.
The Milan players were fuming over Dutch referee Bjorn Kuipers and his decision to penalise Alessandro Nesta for pulling Sergio Busquets's shirt at a corner for the second penalty.
"Barca don't need these things. They are the best team in the world," said Swede Ibrahimovic, who left Barcelona under a cloud in 2010.
"I start to understand Jose Mourinho when he talks about what happens when you come here to play against them. Now I have seen it first hand and I understand it more and more."
Real Madrid coach Mourinho has accused Barca of getting preferential treatment from match officials in Europe.
Barca coach Pep Guardiola dismissed the idea there was any doubt over either penalty when asked about Ibrahimovic's comments.
"I have seen replays of both incidents and they were clear penalties," Guardiola said.
"Ibrahimovic wants to make friends with Mourinho, but it is now five times in a row we have made the semi-finals. We do our talking on the pitch.
"We deserved to qualify and we are very proud to be in the semis for a fifth time.
"We had 21 shots on target and that against an Italian team."
Barcelona will play the winners of the quarter-final tie between Chelsea and Benfica which the London side lead 1-0 going into the second leg at Stamford Bridge on Wednesday.
"I have no preference for the semis, the two teams would both be very tough," Guardiola added.
Milan boss Massimiliano Allegri admitted that the best team had won, but he was not happy with Kuipers' decision either.
Allegri said: "The best team has qualified. We committed a terrible error for the first penalty, the second is more dubious and the referee gave it too quickly."