The former captain has called time on his 14-year Three Lions career after England's group-stage exit from the World Cup in Brazil.
Hodgson will remain in charge of the side and Gerrard is confident that 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 won 114 caps for England, scoring 21 goals in the process.