Hart has already pocketed two Premier League medals with City but they were powerless to stop Chelsea marching to the title last season.
With the champions in big trouble this season, Arsenal and Manchester United have emerged as City's main title rivals.
Ahead of Saturday evening's game with Liverpool, which City are 5/6 to win, the England stopper says the dynamics have changed at the club since he joined.
"When I first came here league status was important, getting a good, solid base on which to build on was the mind-set," he said.
"Now finishing second isn't good enough. It's a big jump but it's realistic. We should be disappointed when we don't win. We were very disappointed last year and it's a great mentality to have in this league."
Man City are 11/8 to win the title this season as they go into the weekend level on points with Arsenal.
Hart says Manuel Pellegrini has the squad to target victory in every single game and he says there will be hiding place if they fail to win the league.
"We feel like we should be going into every tournament as a favourite, we should be winning games, we feel strong that we can put a good team out.
"At the same time, we have no excuses. When we don't win we have to take responsibility for that. It is exciting going into tournaments and competitions thinking we have a good chance of winning them," he added.
City have conceded just nine goals in 12 league games this season, something Hart attributes to a collective effort.
"I'm the first one to admit that it's all about the team," he said. "I've not had an overly busy season. It's mainly been about communication and having a good relationship with the back four. I think defensively we've been fantastic," he said.