The Brazilian club got the better of the European champions thanks to a 69th minute goal from Paolo Guerrero and although Cahill praised Corinthians for their tactical nous, he felt a few decisions cost his side a possible victory.
"The whole game felt like we were up against it to be honest but I don't want to make excuses," Cahill said.
"Corinthians were tactical, they were well-organised but I don't think we were very fortunate with quite a few decisions on the night.
"We had a few chances with which we maybe could have put the game to bed, it is obviously disappointing. I don't think we played as well as we did in the first game and ultimately it is us that ended up losing the game, and it is the worst feeling in football."