Redknapp launched a blistering attack on the FA earlier this week for ignoring public opinion, stating: "I wouldn't trust the FA to show me a good manager if their lives depended on it."
The QPR boss revealed he had received the support of a number of senior England players in his desire to be appointed Fabio Capello's successor, including Rooney.
This has been confirmed by the Manchester United forward.
However, Rooney now claims he would have been wrong.
"At the time Harry was doing a tremendous job for Tottenham," said Rooney.
"I remember tweeting about it; Harry Redknapp for England. Everyone thought Harry he was nailed on.
"But, as players, we don't get involved in the selection of the manager. Roy has popped up. The FA went with him and I feel it is the right decision.
"It's probably the most I've enjoyed working with any England manager and I feel he's going to take us to the World Cup."
As was the case with Brian Clough, whether Redknapp would have been a success will probably never be known.
The assessment of Hodgson cannot be made until England's present qualification fate is over.
But, looking ahead to Friday's showdown with Montenegro at Wembley, Rooney insists it is already a more enjoyable experience than the austere Fabio Capello regime.
"It is a big difference going from an Italian manager and Italian staff, to an English manager and staff," said Rooney.
"I felt that was really needed. Roy's man management is really good. He always speaks to us.
"He's shown a lot of trust in me both on the pitch and off the pitch, which I've enjoyed."
Hodgson does have a reputation as a cautious coach.
And England's performances under him have not pleased everyone, even if he has made his peace with Gary Lineker, who accused England of heading back to the dark ages with what the former striker deemed were negative tactics to earn a point in Ukraine last month.
"He is entitled to his opinion," said Rooney.
"I was at home for the Ukraine game. I saw all the stuff that was in the press beforehand. Then it was all 'it doesn't matter what the performance is like, if we come back with a draw it's a good result'.
"After the game it was a different story.
"In some games you have to be cautious. It would be silly to play with four forwards or just go for a game when you know the opposition strengths are getting behind your midfield.
"That's part of the tactics that are going to get us to the World Cup."
Reduced to its basics, another would be just to get the ball to Rooney.
After all, with seven goals in his past eight England games, he is clearly the player who has most chance of securing those priceless victories against Montenegro and Poland the following Tuesday that would confirm World Cup qualification.
It would also take him another step closer to getting the additional 14 goals needed to eclipse Sir Bobby Charlton's all-time record of 49 and become the first England player to reach a half-century.
"I believe I can do it," he said.
"I actually feel as though I should have scored more for England. I just want to keep playing and helping the team.
"If I get to that 50-goal mark it would be unbelievable achievement.
"There is a long way to go but obviously it is an aim."