Matt Tubbs, who had earlier put the hosts in front, saw his spot-kick saved by visiting keeper Scott Flinders.
And it proved costly as goals from Charlie Wyke and Marlon Harewood gave Hartlepool the three points.
Dons boss Neal Ardley said: “I am going to take the disappointment because it was another home game against a team down there and that was something we could not see through last season.
"I thought this group would be able to turn that on its head and at half-time we were on the way to doing that. When you look back on it we could have scored four or five goals today.
"We’ve got a group of good players who will score goals, but they didn’t today and we cannot use that as an excuse."