The Tykes produced an impressive performance to secure a 1-1 draw at Portman Road. Substitute Danny Rose netted their late equaliser after Luke Chambers' opener for the Tractor Boys.
But it was no more than the second-from-bottom visitors deserved after an impressive display.
Flitcroft, taking charge for the first time since being appointed full-time, 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."
Town boss Mick McCarthy said of Barnsley's leveller: "We didn't defend properly but they deserved a point.
"Not that I'm happy about it. In fact, I'm very unhappy about it but they deserved it.
"They were the better side and took the game to us. They didn't sit back and try and catch us on the counter.
"We would have nicked it if we'd taken the three points and I'd have been delighted. If you're the inferior side and you get in front, you've got to grind it out. That's how you progress.
"We'll take the point, put it in our pocket and keep it and make sure we keep picking up more."