City's fast rise to the top has seen them secure two pieces of silverware in the same number of years, lifting the Premier League trophy last season and the FA Cup the campaign before.
After getting a taste of trophy success with the club, Hart insists City must continue their ascendancy.
The England No.1 told The Sun: "We've got two trophies and you do start to get a taste for it.
"We need at least one every year now - otherwise it's a failure. Having won something for the last two years it would feel weird now not to win anything. We have to keep it going.
"We want to retain the title, of course but there are the cups as well. We didn't do so well in Europe last season or the domestic competitions, so that's an area where we can improve."
City beat fierce local rivals Manchester United to the league title on goal difference on the final day of last season and Hart expects their neighbours to respond strongly.
Hart said: "They generally react well - of course they'll be a threat to us.
"They're a great side, great players, a great club. But there's a mutual respect despite the rivalry."
The keeper knows things could have been very different had Sergio Aguero not scored his vital last-gasp winner against QPR on the final day of last term to seal City's title success and deny Manchester United a 20th championship.
He added: "It's all a bit of a blur. I've watched the goals back but not the whole game.
"It was a bit of a depressing blur to be honest until the very end. For about 15 minutes during the game - and it felt like three or four hours - I was thinking what effect it would have on the club if we didn't win the title.
"I was thinking I was going to be a horrible person to be around, and what a waste of time the whole year would have been.
"It would have been a horrendous summer, but we got there. It was chaos after Aguero's goal, but now we are just looking forward to getting it on again.
"For a while we felt like we were the most important people in the world but things move on."