The former Reds forward angered many Liverpool fans by insisting he wanted to leave the club after turning down a lucrative contract offer to remain at the Anfield club.
But Hodgson is convinced the experience will benefit the 20-year-old in the long run as he prepares for the new Premier League campaign as a Manchester City player.
“He was playing for a club with a very strong fan base, not only in England but in other parts of the world,” said Hodgson.
“Unfortunately for him, I suppose, the fans locally at Liverpool took unkindly to the fact that he made it clear he wanted to move.
“That is part and parcel of football really. I think if anything that will help him to mature and improve even more.
“I think for his age he is a remarkably strong and robust person, not just physically on the field but mentally.
“And these things, if anything, will make him stronger. He has got a big price tag to carry around, but I think he is a good enough player to do so.”
Hodgson also praised Sterling’s “exceptional talent” and insists he will be part of the England set-up for years to come.
“We have had a lot of faith in Raheem Sterling. He has never been out of our thoughts at any time, whether he has been playing well or not playing well or in the team or not in the team,” added Hodgson.
“We have always had him in our 25 as a player for the future who we think, if we are ever going to become a really good team, we need players like him because of his exceptional talent.”
Hodgson also expressed hope that the injury suffered to another summer City signing – Fabian Delph – would prove not to be too serious.
The former Aston Villa player lasted less than 20 minutes of his debut against Real Madrid and left the field on a stretcher with a suspected hamstring problem, which is currently being assessed by City’s medical staff.
“I don’t know quite how severe that injury is,” said Hodgson.
“We don’t play until September. We are still in July so one hopes it is not going to be an injury which keeps him out until September.”