In his autobiography, Redknapp claims English football was being “run by people who really haven’t got a clue” after losing out to Hodgson in the race to succeed Fabio Capello in 2012.
But Bernstein rejected the criticism and told BBC Sport the timing of his comments – ahead of two key World Cup qualifiers for England – was both “disrespectful” and “unhelpful”.
England, who top Group H, face Montenegro at Wembley on Friday and then Poland away on Tuesday and will secure a place at next year’s World Cup in Brazil with two victories.
“We spoke to up to 20 people within the game: other managers, players, all sorts of people with great, great knowledge”
“To come out and effectively criticise a process and another manager – because that is what he did – at this particular time where we had two crucial international matches coming up was something that I thought someone like Harry would think better of,” said Bernstein, who stepped down from his FA role earlier this year.
Redknapp also wrote: “Everyone said I was the people’s choice, the only choice. All the senior players seemed to be up for me to get the job.
“But the FA went for Roy Hodgson to be the England manager – a man who is more their cup of tea.”
However, Bernstein insisted the FA had done “a very thorough job” when choosing Capello’s successor in May last year and defended the four-man selection panel.
That panel, chaired by Bernstein, also included Sir Trevor Brooking, FA general secretary Alex Horne and Adrian Bevington, managing director of Club England.
“First of all, it’s quite simply inaccurate,” said Bernstein, addressing QPR boss Redknapp’s claims that the FA was “clueless”.
He added: “There were four people who made this decision. 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.
“[There was also] Sir Trevor Brooking, who has a lifetime 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: other managers, players, all sorts of people with great, great knowledge.
“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.”
When asked if Redknapp was a contender for the job, Bernstein said: “I won’t answer that question.”