Chelsea caretaker Di Matteo, who Hodgson succeeded at the Hawthorns, refused to take any credit for the 64-year-old's appointment by the Football Association.
Di Matteo, who had also backed Harry Redknapp's claim to the role, said: "The two candidates, I think, were Harry and Roy, and two very, very good candidates for the England job. Roy is a gentleman, is a very good coach, a very good manager. It'll be difficult for anybody but I think he's got all of the experience that you need for a national team."
He added: "That doesn't take anything away from Harry's job that he's doing or has been doing over many, many years."
Asked if Hodgson was underrated, Di Matteo said: "From his fellow professionals, he's certainly not.
"Within the game, I think he's highly rated. I'm not sure about public opinion but, certainly, he's a fantastic manager.
"I think that he has a lot of respect in every country. He's worked in Switzerland and Italy and England. He's a true gentleman as well, he's a very nice man, and he's always brought results wherever he's worked."
Di Matteo was controversially sacked by West Brom in February last year after getting them promoted to the Barclays Premier League.
Asked if he deserved some of the credit for Hodgson's England appointment, he said: "No. Listen, Roy has got so much more experience than me in what he does in his job and he has moulded a team that is a very good Premier League team.
"The credit goes to the players at West Brom and to Roy Hodgson and everybody there who has worked with him at the club."
Source: PA
Source: PA