The England number one produced a fine save in the dying stages to hold onto all three points for the league leaders as they picked up a narrow 1-0 victory at Villa Park
The game was finely poised following City's opening goal from Joleon Lescott and, as time ticked away, Hart made a great reflex stop to keep out Darren Bent's volley to keep the scores level.
"This season is why they’re talking about [Joe Hart] as the world’s best," Gareth Barry told Sky Sports.
"It’s not just today, every game he’s making one or two great saves; he’s going to be around for a long time, he’s going to be England’s number one for a long time, so good luck to him."
Barry also insisted that it was a "massive" three points to take them back to the top of the league following Manchester United's victory over Liverpool, and admitted that the pressure had been on them to respond with a good result.
"It’s always difficult playing second throughout the weekend," he added. "[Manchester United] have obviously put a bit of pressure on.
"Any away game in the Premier League is really tough, and to come to Villa Park is a massive three points so we’re delighted today.
"We’ve got to back ourselves. They’re a club who has won many championships recently.
"We’re a team full of experience with people who have won championships elsewhere – we know what it’s all about, the manager knows what it’s all about, so we’ve got to use that experience to get through now what is the business end of the season."
Barry played a key role in the only goal of the game as he nodded James Milner's corner back across goal for Lescott to convert, but he stated that his team had initially been worried about the threat of Aston Villa from set-pieces and had not targetted them specifically in attack.
"[We didn't target set pieces], if anything with the team we had out we were slightly worried about the height that they had.
"They had a couple of chances from corners and it was probably a bit unexpected that we got the winner from our corner. But any goal and three points at this stage is massive."