A Michael Keane own goal and one from Sheffield Wednesday loanee Chris O'Grady ensured the Tykes climbed back out of the bottom three at the first attempt after their 2-1 defeat to the Owls on Saturday.
Striker Jason Scotland had a second-half penalty saved by Kasper Schmeichel and Flitcroft insisted it could have been a lot more.
"It could have been four, five, six. The two goals, I'd love to see them again. The passing, the intricacy - wow. I wish we were watching them on telly tonight," he said.
"We could have been talking about a huge scoreline because that's how much we dominated Leicester today. We were brilliant.
"The top teams want to play you, they've got great players. Leicester are a team of superb individuals but we didn't let them play today.
"I've talked a lot about the fight and the spirit in recent weeks but today I'm talking about the football. It was a relentless approach.
"It's an honour to be a manager on a day like this. Our football was just exhilarating.
"If I'm being honest I didn't expect us to get up to those kind of levels after being bombarded on Saturday."
Flitcroft picked out O'Grady - who made it three goals in nine appearances since joining the club back in February - for special praise.
"Chris O'Grady gave an absolute masterclass up front. If we'd have seen that in a more fashionable team we'd have been raving about it for a couple of weeks. It was just a pure masterclass," he said.