Substitute Jamie Vardy struck home from close range after good work from David Nugent at the death to stretch the Tykes' winless run to 10 games.
The South Yorkshire side led 2-1 at the interval after goals from Stephen Dawson and Reuben Noble-Lazarus had cancelled out Anthony Knockaert's early opener.
But they were unable to hold out for a shock victory when former Fleetwood striker Vardy beat Luke Steele from close range for a share of the spoils.
Flitcroft said: "It was very disappointing to concede the late equaliser but at the same time there was a sense of pride that we had taken a point against one of the best sides in the league.
"Leicester are a team I think can win the Championship, so it is a real positive to have earned something against them. We came here with a game plan to press them and be in their face. We knew we had to match them, and I thought we did.
"Our goalkeeper Luke Steele was incredible early on, and then we scored the two goals that I felt were deserved."
He added: "I think that, as a group, we are coming together but at the moment we are just missing that last little bit. In golfing terms we are getting on the green well enough but missing our putts. The aim at the start of the season was to stay in this division - and it still is."
- Sports & Recreation
- Luke Steele
- Jamie Vardy
- Stephen Dawson
- David Nugent