The former Tottenham Hotspur coach was critical of the FA after missing out on the Three Lions job, but has now conceded that Hodgson was "better qualified" for the post.
"They made a good choice. Roy's an excellent manager and nobody disputes that," he told BBC Sport.
"Looking at it he was better equipped and better qualified, maybe at international level, than I was. I don't want to dispute that. He's a very well-qualified guy.
"I haven't got a problem with Roy. I'm delighted he's doing well and no-one is disputing the choice of Roy as manager. I really am not."
However, Redknapp is standing by his criticism of the FA, maintaining that the governing body needs more "football people" on board.
"All I'm saying is I do believe the FA in general they need more football people involved," he added. "They have picked a few managers in the last 20-odd years or so who were lucky to manage England."