Bernstein also insisted he had no regrets about standing up at the FIFA Congress this summer to call for Blatter's re-election as president to be postponed.
Blatter stood unopposed after arch-rival Mohamed Bin Hammam was forced to pull out of the race amid bribery allegations against the former president of the Asian Football Confederation.
It was one of several corruption scandals to engulf FIFA in recent years and Blatter promised to reform the organisation, with an announcement about how he intends to do this due on October 21 following a meeting of the organisation's executive committee.
But speaking at the Leaders in Football conference in London on Wednesday morning, Bernstein said: "We had a UEFA strategic meeting two weeks ago in Cyprus and there was great disappointment expressed there about the lack of progress that FIFA are making in terms of governance.
"There is a FIFA ExCo this month and we are hoping something will come out of that but I wouldn't hold your breath.
"It's a difficult nut to crack, we will just have to see what Mr Blatter will do."
Bernstein would not go as far as England 2018 World Cup bid chief Andy Anson, who ridiculed FIFA's handling of recent scandals and labelled Blatter's desire to enlist the help of opera star Placido Domingo as "laughable".
Indeed, the FA chairman insisted his organisation's relationships with FIFA and UEFA had improved since the latter tried to prevent his intervention at the FIFA Congress.
He added: "I wouldn't say it was foolhardy.
"There was a momentum of events and I felt I had to say something.
"The morning of that session, UEFA held an emergency meeting to discourage me from saying something.
"I said that within English football there are plenty of disagreements but everyone has the right of free speech.
"I would definitely do it again."
Bernstein also revealed Argentina's FIFA vice-president Julio Grondona had apologised for his "unacceptable" attack on England at the FIFA Congress.
Grondona, who is also president of his country's national association, branded the English "liars" and "pirates" in June, but has now written a letter of apology.
Bernstein said: "I was pleased to receive a letter of apology from the Argentinian (FA) president Grondona following his unacceptable comments about England in Zurich."
Bernstein promised the FA would get its own house in order after the recent Parliamentary Select Committee inquiry into Football Governance urged the Government to legislate if the game's governing bodies failed to adopt new practices.
Bernstein said: "If we can't then there is a danger that they will legislate.
"Our job - and that's why we're working so closely with all our friends at the Premier League and Football League and the national game and others - is to make sure that doesn't happen."
He added: "The Select Committee report is not perfect. I think there are parts of it that leave something to be desired.
"But there is merit within there.
"We have to pick the best bits, work out a package that we can deliver together and come up with something so that the Government doesn't have to get involved."
One Select Committee criticism centred on the lack of diversity within the FA, who are set to appoint two new independent directors to their board.
Quizzed about the prospect of a woman being selected, Bernstein said: "A woman on the board would be wonderful if we could find the right woman.
"In all these things, we want the best people.
"I don't think we should be absolutely governed by definitions.
"If the best includes diversity, I think that's fantastic."
Bernstein did admit more ex-players were needed within the organisation, saying: "We should see more footballers coming through the organisation.
"I think it would be fantastic."