Sam Winnall scored in each half for the in-form Iron but was shown a second yellow in the 68th minute after celebrating his second goal with the travelling fans.
Chris Sedgwick swiftly pulled one back before Dan Nardiello, on loan from Rotherham, equalised in the sixth minute of stoppage time to prevent Scunthorpe joining Chesterfield at the top of League Two.
"That emotion in the last 20 minutes, we'll take that away from the game," said Flitcroft. "But I don't want to spend 20 minutes of the game recovering.
"The first thing I asked the players to do was to commit to a clean sheet at half-time. We lasted 39 minutes but again our Achilles heel came back to haunt us.
"I said to certain players at half-time that they needed to stand up and be counted. They were just going through the motions but in the last 20 minutes they came through that.
"There was a force and a fury about our play. Scunthorpe defended defiantly but I thought we deserved a point."