Cahill dribbled the ball out of defence, but he lost possession, the ball rolled to Fred, and he beat Joe Hart from 18 yards.
Hodgson chose to keep Cahill on the pitch and the move paid off as he tightened up at the back and he then almost grabbed England's second with a point-blank header which Julio Cesar did well to save.
"I thought he played well before and after (the mistake)," Lampard said of his Chelsea team-mate.
"He is a perfectionist. He is a very, very good defender.
"I was chatting to him in the dressing room after the game. I told him not to worry about it. He made a mistake and when you do that you have got to stand up again and be outstanding and he was so we can forgive him for that."