The England number one earned those plaudits after a stunning performance for City in their Champions League draw with Borussia Dortmund at the Etihad Stadium last week.
But the 25-year-old, speaking ahead of Friday's World Cup qualifier with San Marino at Wembley, admits he is determined to scale even greater heights.
Hart said: "It's nice people say nice things but things are easily said.
"In goal, you can be the worst in the world two days later if you are on television and something mad happens in the game.
"You've got to try and take the rough with the smooth.
"It was great and a real special honour for some special people to say some nice things but we move on.
"You've got to remain level-headed. If you don't, it's a big slap when you do something wrong. Then people are going to say bad things about you but that's football.
"You can't go too far one way or the other or you leave yourself vulnerable."
Hart admitted: "I'm still trying to improve. I hate to say it but I am getting a bit older now so I have to get in a bit earlier and prepare my body a bit differently.
"I just know every day I want to be the guy you can rely on. I want to be the best.
"I want to work hard on saving every shot. Pretty simple really. I've got no silly targets like I need to win this and I need to do that.
"I need to keep working hard, keep my love and passion for the game and hopefully good things will come."
Hart admits concentration is paramount as the solidity of the Manchester City and England defences means he has long spells when not called into action.
He said: "It's just not often that I get much opportunity to make many saves because we are so solid at the back.
"Concentration is always key. International football is not often 'you have a go and then we'll have a go'. It's a chess game.
"I imagine, like most teams when they come to Wembley, San Marino are going to try and get people behind the ball."
With Steven Gerrard suspended and Frank Lampard doubtful with a knee injury, there has been speculation Hart could skipper his country against San Marino.
But Hart believes the honour will go to Manchester United striker Rooney.
He said: "I've not thought about it at all. How the captain is chosen is the manager's decision.
"I've got a big responsibility to keep my place in the team for club and country.
"If I do get the nod, I'll try and give as much as I can in terms of helping the team.
"But I think it's between Wayne Rooney and Wayne Rooney if we are going to go on experience and how captains have been chosen in the past."
Hart knows England have to ensure no slip-ups during the remainder of their qualification campaign after the home draw with Ukraine last month.
He said: "We really need to push on from here. You have got to look to win all your games until you have potentially qualified.
"In the group stages, when you are qualifying for a World Cup, you know there is so much for the taking but there are not that many games and you have to get things right.
"We'll start by trying to do that on Friday after a good battling point against Ukraine in the last game."