The England captain cut a disappointed figure as Manchester City clinched the Premier League title on the final day of the season, with his costly slip-up against Chelsea in late April proving to be a turning point.
Gerrard, 33, was named in Hodgson's 23-man squad on Monday and the Three Lions boss hailed his skipper ahead of the tournament in Brazil.
Hodgson said: "I have no concerns whatsoever over Steven. I'm very disappointed for him of course. I'm very sad that he feels himself responsible for the mistake he made.
"But Steven is extremely mentally strong, and extremely proud. He loves Liverpool but he loves England and I don't have any doubt that he won't be as good as he ever has been in this World Cup."
Hodgson named a youthful England squad that included eight players under the age of 24, but he also named experienced internationals Frank Lampard and Wayne Rooney alongside Gerrard.
And the former Liverpool manager said he is excited by the number of options available to him in a versatile attacking set-up.
"There are certainly people who are regulars who most people would expect to start but so much has happened in the seven months since we qualified - so many players have burst onto scene," he said.
"In the front six we have a lot of options and possibilities and a lot of players who can play in different positions and it's exciting.
"Whereas in the back-four and the goalkeeper we will be a lot more stable and it might be easier to second guess my selections."