The Blues had the better of proceedings against the second-placed Foxes, but failed to make the lion’s share of possession count.
Hart said: “It’s a game we could and should have won but we didn’t. Kasper Schmeichel did well and made a few good saves but we maybe should have done better with the chances we had.
“We’re not where we should be right now in the table, but we’re right in the mix without really playing that well.
“We started the season strongly but we’ve not been great over the last 12 games or so but we’re in a good position and the two teams above us deserve to be there.”
Hart added that the only way to put pressure on the teams above was to string a run of victories together – something few teams have managed to do in what is proving a topsy-turvy Premier League this season.
“Without doubt, to push on, we need to win – win all our home games and be damned hard to beat in our away games as well.
“We need to take victories where we can and enjoy it with our fans who were fantastic again tonight.”
Team-mate Raheem Sterling, voted man-of-the-match after an industrious performance, also felt the Blues’ endeavours deserved more, adding: “I thought we played really well at times - obviously Leicester had their moments, too, but feel we controlled the majority of the game and had a few chances to score.
“They’re a good team and kept us out and that’s what this league is all about and hopefully we can bounce back and win our next game. The only thing missing tonight was a goal.
“On the positive side, it was important to come here and keep a clean sheet, which we’ve achieved, and we defended well as a team. We haven’t been playing that well away from home lately, but we’ve come to a team who are second in the table on merit - I think we played well overall and now we’ll move on to the next game.”
“We just need to focus on ourselves, win as many games as possible and hope that’s enough at the end of the season.”