Harper hopes the West Ham keeper is given the opportunity to repair the damage and his reputation in South Africa.
He told The Journal: "You can either go and sit in a dark corner of a room somewhere and beat yourself up about it, or you can get out there on the training pitch and get on with things. I'm sure Rob is doing the latter.
"He also showed great mental strength after the game to come out and speak to the media. He is a strong character and I would like to see him keep his place against Algeria.
"I would stick with him. If Fabio Capello drops him on Friday then it will destroy his confidence and it is something he may never recover from as an England player.
"He's a good goalkeeper and we must not forget that just because he has made one high-profile mistake.
"If he takes him out of the firing line now that will be it for him at this World Cup and it is going to be a long wait until he gets the chance to put it right, probably when West Ham play their first game in the Premier League."