City was beaten 2-1 by the Catalan giant in the first leg of the last-16 match-up - after Clichy was sent off - but Hart prevented further damage in injury time.
Hart saved a spot-kick from four-time world player of the year Messi and then watched in relief as the Argentine, who had otherwise been brilliant, headed the rebound wide.
City will still face an uphill task in the second leg at the Nou Camp - and Clichy will be suspended - but the Frenchman hopes the momentum has now shifted to the Premier League side.
He said: "We always say you have to look for positives and I think this save was a massive one.
"I am not talking about the quality of Joe - because he is one of the leaders in the dressing room and on the pitch - but this save could be the turning point.
"I am not saying it's going to be easy, and you cannot say this save is going to make us win the game.
"But, for sure, 2-1 is a different score to 3-1 and we have to look forward.
"We have the quality to do something and we are going to try our best and hopefully get something out of the game at the Nou Camp."
City was overrun in the first half and fell 2-0 behind inside the first half hour as former Liverpool striker Luis Suarez struck twice on his return to England.
Neymar had an effort cleared off the line and Dani Alves hit the bar, while Messi simply teased the City defence with great regularity.
City responded after the break and pulled one back through Sergio Aguero but it was left hanging on after Clichy was dismissed for two bookable offences.
His second yellow card, for a high challenge on Alves in the 73rd minute, seemed harsh and Clichy, who was slow to leave the field, felt he was unlucky.
The 29-year-old said: "If you play by the rules, they are probably two yellows, but I have done two fouls during the game, and I wouldn't even call them big fouls.
"So probably after the first booking, if I had made four or five fouls and the ref is saying, 'Okay, the sixth one is enough' that would have been fair.
"But it was only my second one, and they made some fouls as well, probably worse than mine, and didn't get booked.
"Those fouls in England are not bookings, but we were in Europe. That's the way it is and I can't complain because, by the rules, it is probably two bookings.
"At the end they got a penalty. It was probably a penalty, but it was still a big decision.
"But the game is not over."
