City beat Chelsea on Sunday, who are now seven points behind them in third place and asked if the champions will continue to look up rather than down, Hart said: "Yes, you've got to.
"It's going to be really hard, we've got a lot to do but we're going to have a damn good go at doing it."
The 2-0 win was City's first in the league since the 2-0 home victory against Fulham on 19 January. "It's big, but it is what it is. You can speculate and talk about the past but we have just got to look forward and try to win. The only way is up for us," Hart said.
The goalkeeper underlined the side's unswerving belief. "Even if there is one game to go and we are 12 points behind, we'll still believe," he said. "We've got to. We've got to keep fighting, you never know. We have just got to keep going."
The previous league outing was the 3-1 capitulation at Southampton a fortnight ago which moved Roberto Mancini to criticise his team.
Hart believes the performance against Chelsea is evidence of City's spirit. "We have got it, no doubt about it," he said. "We all underperformed against Southampton – that's gone, you can't do anything now, you move on from that. You have got to look forward."
Hart praised City's determination to keep going and beat Chelsea, with Yaya Touré not opening the scoring until the 63rd minute before Carlos Tevez confirmed the win near the end. "That's why I love football. You can't not love it," said the goalkeeper. "The mood when the goals went in, and stuff changed, you can't buy it anywhere else. I really do think we are united as a group – the players feel the fans and the fans feel the players. We do it for them. Once you are in that atmosphere, in that bowl, you are as one."
Hart also praised Jack Rodwell, who in a first start since 1 September because of hamstring problems, offered an impressive performance before being replaced early in the second half due to tiredness. "It is nice to see Jack [play well]. I am really happy for him. He's a really good boy," Hart said. "It's been hard for him, he's been injured a lot but when you get him fit you get good performances.
"Whatever Jack needs to do, whatever he needs, this club will give it to him. Be it fans or players, we're there for him. Hopefully he'll get a little run of games together and we will see what he is about."
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