Barca's players and bench also complained about what they thought was handball inside the box by Inter defender Acerbi and a foul by fullback Denzel Dumfries on Gerard Martin in the build-up to the equaliser which took the game to extra time.
“I don't want to talk too much about the referee, but every decision that was 50-50 went \[Inter's\] way,” German Flick said.
“I am disappointed, but not with my team. They tried everything. It's the way it is. We are out, but next year we will try again to make the fans happy.
“It makes me sad — my team did an excellent job. I don't like talking about the referee — I've told him what I think, but I'm not going to say it here what I've said.”
Barca were chasing a treble after winning the Copa del Rey, but will now turn their focus to LaLiga, where they top the table and on Sunday host rivals Real Madrid, who trail them by four points with four games to go.