The 34-year-old called time on his Three Lions career on Monday but leaves England following a disastrous World Cup which leaves them 20th in the Fifa world rankings - their worst since 1996.
Hodgson will remain in charge despite a group-stage exit in Brazil and while Gerrard admits the opinion on England is "very negative" he is confident the former Fulham boss was the correct appointment.
"I'm sure Roy will get the job right. I know things will turn around for the better," he told reporters. "I know the players are upset and everyone has an opinion on England at the moment - it's very negative.
"But I'm sure Roy will help making the England supporters proud again and change the way people are looking at this England team.
"He's a fantastic manager and I'm glad the FA have stuck with him. He's the man who fulfilled my childhood dream, made me England captain, and I'll always thank him for that."
Gerrard does not expect his ties with England to end after 114 caps for his county and left the door open for future involvement behind the scenes as he begins considering his options for when he hangs up his boots entirely.
"I've started the C Licence on the coaching side of it," he said.
"I don't know if I want to be a coach, I don't know if I want to be a manager 100%, but what I'm going to do when I hang my boots up completely is something I'm thinking about a lot.
"My relationship with the FA will continue moving forward and I'm sure over the next 20, 30, 40 years, I will work for England again."