Bernstein steps down from his position in July and has told his successor Greg Dyke, the former BBC director general, of his belief in Hodgson. Hodgson has another three years left on his England contract, and has come in for some flak after recent results and performances, and World Cup qualification remains by no means certain for the national team.
But Bernstein, speaking in Rio de Janeiro where England secured a 2-2 draw in a friendly against Brazil, said he had faith in Hodgson. He said: "Yes, absolutely. Why shouldn't I? We thought it when we appointed Roy and it is still the case that he brings a lot of attributes to the job."
He added: "His experience, his breadth of thinking and buying into the whole game. We are focusing today on the England first team, but his interest in the wider development, in St George's Park and all the other things for the longer term aspects of English football, he buys into all that.
"I think he has been a first-class appointment and I am very confident that he will bring us back to Brazil."
Bernstein confirmed that he had passed his views on to Dyke.
He added: "My successor will make his own mind up. He is clearly an experienced, strong-minded individual and he will make his own mind up. He will have picked up the vibes clearly. I have met with him and passed on that view to him so the answer to the question is yes."
In terms of English players, Bernstein said only 30% of Premier League squads were eligible for England.
Figures produced by the Premier League however say that in terms of the number appearing in matches the figure was 40% last season with a further 7% being other British.
Bernstein said: "We need more of English players playing in the Premier League and therefore we need more world-class players. That is the real issue. There is the 30% figure that we throw around and Germany is 60% and that is a big big gap. That is the big long term-issue."