The Tykes fell behind early to an Anthony Knockaert opener but produced a stirring comeback to lead 2-1 through Stephen Dawson's 12-yard effort and Reuben Noble-Lazarus's acrobatic effort.
Only a last-gasp equaliser from Jamie Vardy saved the Foxes a point, meaning Barnsley's winless run continue to 10 games.
But Flitcroft said afterwards: "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.
"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."
Barnsley currently sit at the top of the relegation zone with 18 points from their 21 games.