Bernstein has fallen foul of a new rule obliging board members to step down once they reach the age of 70.
An attempt to persuade the FA council to allow an extension was blocked in October, and Bernstein will be replaced in six months' time.
Bernstein, speaking at the launch of the celebrations of the FA's 150th anniversary, insisted he would not try to find a different role within the organisation.
He said: "I'm a believer in clean breaks, to be honest. When I left Manchester City, I made a very clean break and I don't want to be spectre at the feast so I doubt it.
"Quite frankly, I'm not even thinking about that. There is six months ahead and it's a really busy six months and I would like for it to go as well as the previous two years."
Asked if he was frustrated at not being able to stay longer to complete his mission to reform the FA, Bernstein replied: "A little," adding that there was lots more he wished to achieve.
One area where progress has been slow is in terms of bringing in the changes reforms to the organisation recommended by the culture, media and sport select committee, such as reforming the antiquated FA council, slimming down the board and bringing in a new licensing system for clubs.
He added: "I'd of course love to see the England team continuing its progress in the World Cup qualifiers - that is absolutely crucial. We are the Football Association and football has to rate very highly.
"I'd like to see us implement the anti-discrimination programme we have now put in place.
"I would like to see some FA governance progress in response to the select committee. So far it has been slower than it might have been.
"I would like to see in general terms more progress on the Respect issues, whether it be player-on-player or player-on-referee, crowd issues or so on."
Bernstein was appointed just a week before sports minister Hugh Robertson described the FA as "without a shadow of a doubt" the "worst governed sport in the country".
Robertson today insisted he had no regrets about saying that - but said the organisation had made great strides under Bernstein.
He told Press Association Sport: "No I don't (have regrets). I was asked about the FA's governance arrangements back in 2010 and I replied honestly.
"Since that time there has been some welcome progress but there is still some way yet to go.
"In the 150 years of the FA you will have had better and worse periods, and I think most of us would conclude that the 2018 World Cup bid was a low moment.
"I think it's fair to say they are no longer the worst governing body.
"Since David Bernstein has become chairman he has done exceptionally well in a difficult job and a lot has been achieved. He will be a tough act to follow."
Robertson said the Government could still enforce change on the FA through legislation but he would prefer the sport to embrace the reforms themselves.
He added: "We do have that weapon in our armoury. I would much rather not use it and that football got on and reformed itself."