The Spanish World Cup winner spilled the ball into his own net to hand Arsenal a draw in the final minute of the Reds' Barclays Premier League clash with Arsenal on Sunday.
It was a rare error from the 27-year-old, who was the club's player of the year last season.
"If you are a goalkeeper and you can't live with a mistake you make then you'll never have a career at any level," said Hodgson.
"There is only one certainty in football if you are a goalkeeper, and that is one day you are going to make a mistake which is going to let in a goal. It may cost your team some points. When you put your gloves on you know that.
"If you are a good goalkeeper it doesn't happen very often and more often than not you come off the field with people congratulating you on winning points for the team.
"It was a mistake, he understands that. We feel sorry for him because he took it hard but he is a strong character. Let's hope he's forgotten it as quickly as I have forgotten it."
Source: PA