Northampton manager Aidy Boothroyd blasted Ishmel Demontagnac after the midfielder's red card in their 2-0 JPT defeat at MK Dons.
The Cobblers had a man sent off for the fourth successive away game when Demontagnac ludicrously kicked out at Dele Alli in the first half of the first-round tie.
And the Dons took full advantage as second-half goals from Patrick Bamford and Alli eased the hosts into the second round.
Boothroyd said: "Any manager worth his salt defends his players but there comes a time when players do things that are unacceptable.
"I saw that coming, the tackle that Ishmel had on him from Dele Alli was a red card offence but you don't react like that and you certainly don't go looking for revenge, because the referee is looking for it.
"Yet again a red card is dominating the agenda but it shouldn't because we played a top-six team in League One, we've grown into the game and towards the end of the first half we were looking the stronger team.
"It was about somebody's complete and utter stupidity on this occasion.
"I'm very disappointed with Ishmel but I don't want to be talking about him because I thought there were a lot of really good performances in this game.
"We haven't got bragging rights this season but our club is on the up, there's no doubt about that."