The striker was shown a straight red card for what referee Lee Collins deemed to be an elbow on Will Antwi.
It astonished the visitors, who were backed up by television replays which showed the 28-year-old’s arms were nowhere near the centre back’s head.
The decision did not affect the result, as United were able to see out the remaining 20 minutes to seal a fine 3-0 win, but it could have big implications.
As it was Constable’s second sending-off this season, ‘Beano’ is in line to miss four big games, starting at home to Cheltenham Town tomorrow.
It would be a huge blow for the side, with the striker’s return to form coinciding with a strong run of results.
Chris Wilder was livid with the decision, which he felt stemmed from a clash between the pair moments earlier, when Constable had ended up falling into advertising hoardings at the side of the pitch.
The United boss had no doubt the official had got it wrong and immediately stated the club would appeal.
He said: “I just think the referee has been sucked into a little bit of argy-bargy.
“There was a little bit of a get together when they were in and around the boards and they had a word with each other.
“But the referee looked at it and just absolutely overreacted, it’s frightening.
“He should see through it, if that’s (Antwi)’s standards that’s poor, to get a fellow professional sent off.
“We don’t do that. Damian (Batt) got smashed by a tackle in the first half, but he didn’t roll about.”
It was unfortunate the red card tainted an otherwise excellent afternoon for the U's, who climbed to 14th in the npower League Two table – their highest position for more than three months.
First half goals from Alfie Potter and Sean Rigg put the visitors in control, before Tom Craddock made the game safe after the break.
Aside from Constable, United have no new injury concerns for tomorrow’s game and have Tony Capaldi available after suspension.
Cheltenham head into the game third in the table and will be well rested after Saturday’s clash with Bristol Rovers was postponed by a waterlogged pitch.