Redknapp on Wednesday night moved to play down any notion of a rift with Hodgson, after it was revealed last week that he did not trust the FA to "show me a good manager if their lives depended on it".
The comments were made public when his book was serialised in a national newspaper, with the suggestion Redknapp retained some bitterness after Hodgson was preferred to him when the FA appointed a successor to Fabio Capello last year.
Redknapp has denied any ill feeling, suggesting instead Hodgson was "better qualified", and congratulated the 66-year-old after he steered England to next summer's World Cup finals with a 2-0 win over Poland on Tuesday night.
"They made a good choice. Roy's an excellent manager and nobody disputes that," he told BBC Radio 5 Live.
"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."
Redknapp does, however, believe some of Hodgson's predecessors were "lucky to manage England" as he maintained his criticism of the FA.
The QPR boss believes Hodgson is one of the FA's few successful appointments in the past two decades and said more former players and coaches needed to be involved in the halls of power.
"All I'm saying is I do believe the FA in general, they need more football people involved," he said.
"They have picked a few managers in the last 20-odd years or so who were lucky to manage England."