Loosehead prop Alex Waller was sin-binned late on for a punch, with Northampton in an attacking position.
And the man disadvantage proved costly as Peter Horne went down the other end of the pitch to win it for the Warriors.
Saints had levelled things up at 20-20 through Ben Foden’s try as he added to scores from Dom Waldouck and George Pisi.
But Waller’s red mist moment and Horne’s late try and conversion left Mallinder’s men with no chance of qualifying for the last eight of Europe’s premier rugby competition.
“It’s naturally very disappointing,” said Mallinder. “We came up here to try to get through to the quarter-finals of the Heineken Cup.
“We knew it was a bit of an outside chance, we knew we needed four tries to give us a chance and we came close but not close enough.
“We got a lineout and we had a chance, a very good chance, but unfortunately we showed a little bit of ill discipline and credit to Glasgow for scoring at the finish.
“It was a chance of going through to the quarter-final of the Heineken Cup or to the Amlin.”