The Tykes produced a performance belying their league position and were rewarded by a late goal from substitute Danny Rose.
And Flitcroft is confident Barnsley can play their way out of the bottom three in the Championship table.
Flitcroft said: "It was a hard-earned point. We can't afford to do anything other than go all-out for victories.
"We've got to win games and gain momentum, by picking up three points.
"It would have been catastrophic if we'd come away with no points. We're going to attack teams and put them under pressure.
"We're going to fight them. These players want to do that - that's what we've all signed up for."