The QPR manager concedes that the current Three Lions boss is the right man for the job but still maintains that some of the 66-year-old's predecessors were not up to scratch.
The QPR boss wrote in his autobiography that he did not trust the FA to "show me a good manager if their lives depended on it" but sought to defuse the situation on Wednesday, praising his counterpart's credentials and congratulating him on the Three Lions' progress to the World Cup finals in Brazil.
"They made a good choice. Roy's an excellent manager and nobody disputes that," Redknapp 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."
Despite this, the former Tottenham and Portsmouth manager remains vehemently critical of the FA, arguing that the organization has a poor recruitment record over the last two decades.
"All I'm saying is I do believe, the FA in general, they need more football people involved," Redknapp continued. "They have picked a few managers in the last 20-odd years or so who were lucky to manage England."