The England number one saved a last-gasp penalty from Lionel Messi during last month's 2-1 defeat at the Etihad Stadium and he scaled even greater heights at the Camp Nou on Wednesday.
Barcelona's all-star forward line of Messi, Neymar and Luis Suarez were repeatedly foiled by Hart as Ivan Rakitic's 31st-minute goal sealed a 3-1 aggregate win for Luis Enrique's team.
City fell to Barcelona in the last 16 for the second consecutive season, even though they could have set up a grandstand finish when Sergio Aguero won a 77th-minute penalty.
But Barcelona goalkeeper Marc-Andre ter Stegen kept out a tame spot-kick - much to his opposite number's frustration.
"We’ve gone out to a magnificent side but that’s the second time in two years, which is disappointing for us," Hart told Sky Sports.
"They're going to get a lot of plaudits for how they played - they’ve got fantastic players - but we had a big chance.
"We hung on in there and we had a big chance. Unfortunately we didn't take it.
"You could say they had a chance to finish us off last game but that's how football goes.
"It's just unfortunate after the first leg - it was nice to save a penalty from Messi, I wanted it to count but unfortunately it hasn't.
"I'm in there to make saves. They hit me a lot tonight, I just tried to be big."
In contrast to that modest personal appraisal, midfielder James Milner was happy to lavish praise upon his team-mate for club and country.
"There's not too many words you can say, he [Hart] was incredible really," he said.
"He's shown again what a great keeper he is. It's not the first time he’s done that for us in Europe.
"He gave us that chance, by the penalty they could have been out of sight.
"He was amazing tonight and deserves everything that gets said about him."
On the tie overall, Milner conceded that City fell to superior opposition.
"I don’t think we showed our best over the two legs for long enough," he added.
"We showed it in patches, we stopped them playing in patches, but I don't think we did enough to put them under enough pressure over the whole 180 minutes.
"If you stand off teams like this they're going to keep it all day. We could have pressed them better, for longer, and when we had it I don't think we showed our quality at times.
"You have to be at your best for 180 minutes, not 30 minutes at a time."
