Dani Lopez, whose loan stay from Stevenage expired after the game, swept the Shots ahead from close range in the second minute of Tuesday night's League Two encounter at The Rec.
But Chris Hackett levelled from the penalty spot after Michael Hector had handled in the box, Clarke Carlisle then headed the Cobblers' winner before the break.
"You can't give away goals cheaply like that - it was a reminder we have to do the basics well," Holdsworth said.
"Their goals came from a handball and a set-piece. I thought we were unlucky to go in trailing at half-time but we have to eradicate those errors.
"The conditions were tough for the players but they weren't good for either side. It's very difficult to judge performances in a game like that.
"We got beaten but I'm trying not to be too critical. You couldn't see the best of the players or the potential we have.
"Adam (Mekki) set Dani Lopez up nicely for his goal. He knows where the net is. If that's his last performance we'll thank him and look to replace him.
"I've made my offer to Stevenage with regards to keeping him on loan, but they're entitled to take him back."