Despite defeating Guarani 2-1 in Sao Paulo on Wednesday, Corinthians crashed out on away goals against the Paraguayan side, who last week won the first leg in Asuncion 1-0.
Luan gave the hosts the lead in the ninth minute and Mauro Boselli doubled their advantage after Pedrinho was shown a second yellow card for catching Angel Benitez when attempting an overhead kick.
Nunes' main gripe was with Pitana's decision to penalize Gil for a foul on Raul Bobadilla, awarding a free-kick that Fernando Fernandez guided into the top-left corner from the edge of the box in the 53rd minute.
Guarani had Jhohan Romana sent off for a second bookable offense with five minutes remaining but held on to advance to a meeting with Palestino in the third qualifying stage.
"I would like to thank our supporters, who greatly appreciated the efforts of the players and applauded after the match. And I congratulate the players for what they did, they gave a lot. We created enough to win," said Nunes.
"At the same time, I want to apologize to Brazilian referees for the criticism we've given, even more after facing terrible refereeing by Nestor.
"He's an experienced guy, who knows how to take the game the way he wants it. It was decisive.
"There was a foul that did not happen – Gil did not touch their player. When things get out of our control … it's difficult to make an accurate assessment."
The last time Corinthians suffered the ignominy of elimination in the Libertadores qualifying stages was against Deportes Tolima in 2011.
The fall-out saw Roberto Carlos leave the club due to a fear for his family's safety following threats from supporters, while Brazil great Ronaldo retired days later.
Nunes said comparisons to nine years ago were "not compatible with today" and was keen to absolve Pedrinho of any blame for Corinthians' latest defeat.
"He's not a villain. He is a very important player for our team. The first foul was an accident, the second he doesn't even see, he's trying a bicycle kick but the opponent anticipates it," said the coach.
"How can I blame him? There's no way. He did a lot while he was on the field. He has all our affection. I don't pass the buck. We have to lick our wounds. We know what we need to improve. Hopefully this moment serves as a learning experience."
Vagner Love felt the players could only look at themselves when analyzing where the tie went wrong.
"We apologise to the fans who came here and supported us from the start to the end. The blame lies solely with us, the players," the veteran striker said in a post-match TV interview.
"It's difficult to explain it. We're very sad, we really wanted to be in the Libertadores. We worked hard for it to happen. But, unfortunately, it wasn't our day. At no point did we stop fighting."