Bernstein praised Roy Hodgson's men for putting the smile back on their supporters' faces prior to what was another agonising penalty-shootout defeat last night.
England crashed out of Euro 2012 after losing on spot-kicks to Italy as they once again failed to reach the semi-finals of a major tournament. But they arrived in Poland and Ukraine with many predicting they would not even qualify for the knockout stages, having been without a manager until Roy Hodgson's appointment barely a month earlier.
They defied the doubters to top Group D with seven points and that was enough to give Bernstein encouragement for the future.
Asked if England had put a smile back on the faces of fans, he told BBC Sport: "Yes, we certainly did until the penalties last night.
"That spirit started to grow again, and people started to talk about winning the competition and so on, so we've definitely done that.
"It's disappointing to lose a quarter-final again in the way we have, there's no question of that.
"It's not what we're trying to do, so the glass is half full, let's put it that way, but there's a way to go."
He added: "We came here to attempt to win the competition so that is a disappointment.
"However, I think there's a great deal of positives coming out of this - the performance of the team, the commitment of the team, the togetherness of the squad.
"I think Roy has made a real impact very, very quickly, just the sort of thing we thought he'd do. His organisational skills are very clear.
"He was dealt not the easiest hand at such an early stage but I think he's played it very well, and I think there are positives and I think we have a good base to move forward from.
"The qualities we thought he'd bring, he clearly is bringing.
"You can ask the players and people around the squad, there's been a great feel, and I think, compared to previous competitions, we're a long way ahead of that, in performance as well, not just in spirit.
"We all know there are certain shortcomings in the way we play our game and we need to move forward in that, but that's not a lesson we've learnt today - we knew that before."
Indeed, England had less possession than their opponents in all four matches they played in Ukraine and fewer shots in all but one.
Bernstein said: "It's something we were very well aware of before last night, and the opening of the national football centre this year is a terribly important thing going forward.
"In the youth development scheme the emphasis now is on small-sided football, skill-based football, passing the ball, less emphasis on physicality, all those things which are our agenda already.
"This is not coming from last night, we've worked on this for years, but I think these things are coming to fruition now, so I do expect to see improvements - but it won't happen overnight."
Bernstein was also pleased with how England had performed as "good tourists" at their training base in Krakow after their sheltered World Cup campaign two years ago.
He said: "I think we've done a very good job and a number of very positive things generally, and I think the players have benefited from that, actually.
"They've been relaxed and felt a part of where they are, so I think it's a great improvement on what's happened previously, and a great tribute to the FA organisation."