Ivan Rakitic scored the only goal as Barca secured a 3-1 aggregate win on Wednesday, but the margin could have been greater had it not been for the heroics of the England number one - who saved a late penalty from Messi in the first leg last month.
Hart said it was an "honour" to pit his wits against Messi during a post-match interview, and the Argentina captain returned the praise with a glowing assessment of his opponent's display.
"Joe Hart had an absolutely fantastic game," Messi told UEFA.com. "I already knew he was a top keeper, but it was impressive in this performance how he just stopped everything that came his way, with either his hands or his body - he is a phenomenon.
"The fortunate thing, given all that, was we managed to get through the tie, which was all we wanted, so that we could be in Friday's quarter-final draw.
"These nights are just so tremendous to play in and wonderful for the public to watch, especially when the game is played like this.
"The opposition was full of great players and both teams just try to play really good, open football.
"Both City and Barcelona wanted to be on the ball, to do things with it, and it ended up as a pretty spectacular game."
PERFORMANCEJoe Hart's guide to all-round keeping excellence
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.