The former FA chairman has dismissed the 66-year-old's assertion the England manager was selected by an incompetent panel, but refused to say whether the QPR boss was considered
The QPR boss levelled the accusation in his new autobiography, in which he maintained that he was the players' choice to take over from Fabio Capello before the former Liverpool and West Brom manager was chosen.
And now the ex-FA chairman, who headed up the four-man committee behind the appointment, has hit back at Redknapp's statement.
"There were four people who made this decision," he told BBC Radio 5 Live. "One of them was myself, and I've been involved with running Manchester City for 10 years, and chairman of that club for five years, and have since been involved with the FA and Wembley Stadium.
"[There was also] Sir Trevor Brooking, who has a lifetime in football and also managed, and done a great deal in football; Adrian Bevington, who has huge football knowledge, amazing football knowledge; and Alex Horne, the general secretary.
"We spoke to up to 20 people within the game, from right across the game: other managers, players, all sorts of people with great, great knowledge.
"I believe we did a very thorough job. I was very proud of the way we did it. It was done discreetly and professionally and I believe we ended up with the right choice."
Bernstein, however, refused to comment on whether Redknapp had been considered for the vacancy, adding: "I won't answer that question."