The Tykes rarely threatened as an attacking force other than an early Jason Scotland effort, but the result keeps Barnsley out of the relegation zone and Flitcroft was pleased with the defensive performance.
"I think the experience of Stephen Foster and Bobby Hassell marshalled Glenn Murray really well which you have to do, he is the best striker in the league," Flitcroft said.
"Having two experienced heads in there helped us and it is important down the centre of pitch that you have leaders."
A mix-up with the kits threatened to derail Barnsley's preparations as they had to play in the Eagles' away kit after referee Keith Stroud deemed the Tykes' blue and black away outfit clashed with Palace's red and blue home kit.
"There was a bit of a stand-off before the game as I didn't want my players to not have the Barnsley badge, something they play for every day," added Flitcroft.
"But you realise the sense is probably to listen to the referee and I think it was the right decision.
"He asked us if we could wear our warm-up tops which I didn't think was appropriate so we decided to go with Palace's kit.
"The club has done everything it could before the game to make sure we had this situation right. We spoke to referees in the week and made sure they were happy with the kit and then we got here at 1.30pm and it was all change."