The Tykes appeared to be heading for a crucial win when Chris O'Grady gave them the lead in the second half, but Paul Coutts snatched a point for Derby in the 90th minute.
This result has left Barnsley second from bottom and Flitcroft has urged his players to shrug off this result and make one last push for survival.
"The players are feeling the pressure of the situation, there's no doubt about it," said Flitcroft.
"Don't forget we got downed 6-0 at home [to Charlton on Saturday] and we've had two players sent off. That's still in the back of the players' minds.
"They didn't want to get smashed again.
"It was a brave performance, but we didn't get the result we wanted.
"It's not a difficult one to take, it's just disappointment. It's an emotion we're going to have to soon get over.
"We did enough to win that game tonight, but we're not going to be victims, we'll keep fighting until the end.
"We'll grow stronger over the next few games because we'll get players back from injury and suspension.
"I asked the players to raise their game 20 per cent in the second half, because that 20 per cent would have been enough to beat a real nervy Derby team."