The Shrimpers have now gone eight games since they tasted victory and were forced to settle for their fourth consecutive stalemate against the Buckinghamshire visitors who knocked them out of the FA Cup on December 3.
A repeat of that 2-1 scoreline never looked on the cards as both sides struggled to test the keepers. In fact the match only produced two shots on target - both from Southend - and the 7,452-strong crowd had to wait until the hour-mark for those.
But things could have been different if MK Dons had made the most of a bright start. Wade Small put the ball in behind the Southend defence after two minutes, but goalkeeper Darryl Flahavan got a hand to the ball to deny the on-rushing Aaron Wilbraham a shot.
The Dons were handed a gilt-edged opportunity five minutes later when Blues centre-back Spencer Prior handled Dean Lewington's cross from the left.
Dons centre-back Pablo Mills stepped up to take the spot-kick but put his effort wide, with Flahavan having the goal covered with his dive to his right.
Both sides tried pot-shots in a half that produced little more excitement to warm the crowd until the 38th minute when Wilbraham fired a centre across the face of goal and Small raced in at the far post to hit the post with his shot.
Wilbraham was cursing his luck after 57 minutes when his free header from Morgan's free-kick went agonisingly wide of Flahavan's left post.
The let-off sparked Southend into life and they produced the first shot on target two minutes later. Mark Gower centred from the right and midfielder Luke Guttridge was centrally-placed to stab the ball at Matt Baker, who gathered at the second attempt.
Guttridge was in the thick of the action again on 70 minutes when he turned provider, crossing from the right for Freddy Eastwood to head straight at Baker from 14 yards.
But the Dons nearly had the last say five minutes from time when substitute Nick McKoy's 25-yard shot went inches wide of the top right-hand corner of the net.