Bernstein will leave in July after falling foul of a new rule obliging board members to step down once they reach the age of 70 - and failing to convince the FA council to allow him to extend his term.
Robertson, who one week before Bernstein took over in 2010 described football as "without a shadow of a doubt the worst governed sport in the country", warned it is going to have a tough task in finding a successor of the same calibre. Robertson said: "David Bernstein is recognised as being a really good chairman of the FA."
Robertson, speaking at the launch of the FA's 150th anniversary celebrations, added: "People find it hard to understand why you have a good chairman who is respected and you lose him in the middle of your 150th year. I've been asked by significant figures internationally how that has been allowed to happen.
"In all honesty, a part of this appears to be that he was a reform-minded chairman. Nobody can think it is a sensible idea to change the chairman in the middle of that celebration."
Robertson says the FA are no longer the worst governing body and pointed out Bernstein had been chairman of a FTSE 100 company, a former club chairman [at Manchester City] and had also been a successful chairman of Wembley Stadium.
The minister added: "He had everything you would want and I think he's done really well. If you ask me about the great improvements since 2010 a lot is down to David Bernstein.
"I don't think you are going to find another David Bernstein in a hurry. He's been exceptional. It's a very difficult job. You need a mix of skills.
"He had a pretty unique set of skills. There are some good candidates out there that will have a go but he's going to be a hard act to follow.
"Put yourself in [UEFA president] Michel Platini's position - he's given England the Champions League final again, he has a relationship with Bernstein which has not always been the case with FA chairmen, he's somebody he likes, trusts and rates and suddenly he's plucked out in the middle of the 150th year."
- Sports & Recreation