The Stags looked to have scraped home thanks to a first-half strike from Kevin Sandwith before defending well in the closing stages.
But Moses Ashikodi denied them a first clean sheet of the season - and successive home wins - with a late equaliser as the match ended 1-1.
"We should have had three points. We should have put the game to bed in the first half, but at 1-0 they are always still in the game," said manager Holdsworth.
"We just needed to show a little bit more composure in the final third.
"The players will be down because it feels like you have let two points slip away but you have to take your chances in football.
"The good thing is we are creating chances and we defended very well.
"I can't fault their effort either, which I thought was outstanding and they battled hard. I thought they deserved a clean sheet."