The usually dependable centre-back dribbled out of his own box, Brazil stole possession and the ball fell in to the path of Fred, who slotted the ball past Joe Hart.
"That's the nature of my position," Cahill said.
"I thought I played well overall but if you make a mistake like that it's going to be costly. It was out of character from myself, but I will learn from it and that's great.
"I showed character to bounce back from it and the team showed character to forget about it and carry on.
"Thankfully Frank scored so it didn't spoil the lads' night.
"It did spoil my night slightly though."