The West Ham goalkeeper was grateful for the backing the players received from the supporters.
It has been a challenging season for West Ham so far, with Slaven Bilic having been sacked and there were fears of a further setback against Leicester, especially after David Moyes had overseen his defeat in his first game in charge away to Watford.
There had been chants of "Sack the board" during the Watford game, but the West Ham fans were supportive of their team against Leicester.
Backed by their supporters, West Ham secured a point, with Cheikhou Kouyate equalising after Marc Albrighton had put Leicester ahead.
Hart told the club's official website: “I’d like to say a big ‘Thank you’ to the fans as it could have gone one of two ways on Friday night and they chose to stick with us and we have put a performance in.
“I was stood in goal and didn't have a lot to do second half and it would have been easy to carry on hammering us, but they were fantastic.
“As good as the players are who we’ve got on our team, when we have their support we play differently. I’m not attaching any blame to the fans, but it meant the world to the players."
There is still much work for West Ham to do in order to get out of their current predicament, with the club remaining in the relegation zone, but the response against Leicester will undoubtedly provide Moyes' side with an injection of confidence.
Next up for West Ham is an away game against one of Moyes' former clubs in Everton.
West Ham's following three fixtures are against Manchester City, Chelsea and Arsenal, meaning that it is vital that they pick up points against Everton, another side that have found matters incredibly difficult this campaign.