The striker, nicknamed ‘Beano’, was dismissed for violent conduct in the 3-0 win at AFC Wimbledon after an aerial clash with Will Antwi.
United felt video evidence proved referee Lee Collins had made a mistake, but a disciplinary panel upheld the original decision.
It is a body blow to the U’s, whose excellent run has been partly down to Constable hitting a rich vein of form in front of goal, with six in the last nine games.
The ban starts with the FA Cup third-round tie against Sheffield United and also includes the Johnstone’s Paint Trophy area semi-final clash with Southend, plus npower League Two games against Bradford and Rotherham.
United boss Wilder was extremely frustrated by the ruling, but did not feel the blame rested with the officials.
“Without getting myself into trouble, I think it’s the wrong decision,” he said.
“I’m disappointed for the player and the club because he’s going to miss some big games and he’s playing extremely well.
“It really hurts us.”
United’s hopes rested on the camera footage of the incident proving the 28-year-old’s challenge was not a deliberate, violent act to injure an opponent.
But there was enough doubt in the minds of the panel to reject the claim.
Wilder believes if the game had been played at a higher level, with a variety of high-quality camera angles, it would have been different.
He said: “If that was in the Championship or above, there’s no doubt about it, he would have got off.
“They would have been able to slow the footage down and it would have been clear.
“Now we just have to try and get through this busy period.
“We have had bigger blows and we got over those hurdles. This is another one we’re going to have to clear.”
News is expected shortly on whether United have been able to agree a new deal with Swindon Town for Lee Cox.
His loan expired after the 1-0 win over Cheltenham and although the 22-year-old is keen to continue, there are doubts over his return.