The Dons showed that they are not quite down and out, but they will be kicking themselves that they didn't take maximum points after they dominated the play.
Wayne Gray blew two golden opportunities in as many minutes late on with a blast high over the bar from eight yards out and a feeble shot that was easily blocked.
Patrick Agyemang also came close ten minutes from time when his powerful shot was deflected just wide.
But Megson will be concerned his side's festive blip is turning into a full-blown slump after his side missed a host of scoring chances.
Rob Hulse had an overhead kick saved by Steve Banks 16 minutes into the game, while Thomas Gaardsoe should have scored when he nodded Jason Koumas' free-kick wide.
Koumas wasted an opportunity for himself seven minutes before the break when he shot weakly straight at Steve Banks.
Wimbledon looked more up for the fight than their high-flying opponents, and were unlucky not to turn a ten-minute spell of pressure into a goal.
Jamie Mackie, on his home debut, was the first Wimbledon player to come close after just six minutes when his shot went just wide of the post.
Agyemang and Adam Nowland both came close before Mackie let fly with a shot that just skimmed over the crossbar on 29 minutes, but they couldn't find a way to break the deadlock.