Barca wrapped up a 4-2 aggregate win over two legs on Wednesday with a 3-2 second-leg victory at the Vicente Calderon - which was marred by the sending off of two of the hosts' players by referee Jesus Gil.
It could have been three had Gil sighted Arda Turan throwing a boot in the direction of the assistant referee.
But Gabi said he felt he had not done enough to earn a second yellow card, with the skipper already cautioned heading to the half-time break - at which time he was dismissed.
Gabi was protesting the lack of a penalty awarded when Barca's Jordi Alba was spotted using his arm to block an Antoine Griezmann shot on goal, just moments before Alba helped tee-up Barcelona's third goal of the night - and Neymar's second - in the 41st minute.
"My words were: 'Jesus, it was a penalty and send off and he told me, 'you're out'," Gabi told Canal+.
"That has been my lack of respect towards him. I think he should have much more personality and more dialogue with the player.
"There were 50 people in front of us. That's what happened. I said 'when you see it on TV, you'll see that it was a penalty and send off' and he shouted 'you're out'.
"That's all that happened.
"We all make mistakes. You have to be fair, admit your mistakes and that's it.
"There's nothing wrong with making mistakes but you shouldn't go any further and want to be the protagonist."
Coach Diego Simeone was not rueful of Atletico's defeat, instead hailing a half of football in which they shipped three goals.
"I'm proud of my players. We played an extraordinary first half, with enthusiasm and playing an intense match," the Argentinian said, according to Atletico's official website.
Simeone also spoke highly of their run to the last eight in the domestic competition.
"We played a decent cup. We eliminated L'Hospitalet and Real Madrid. It has been very important because it gave us the opportunity to play against Barcelona," he added.
