The U's, who knocked Plymouth out of the Johnstone's Paint Trophy on Tuesday night after a penalty shoot-out, named Constable on the bench to give the striker a rest and the former Kidderminster man came on and scored Oxford's equaliser.
Manager Chris Wilder handed youngster Tyrone Marsh, 18, his first start after he impressed in training, yet the player is set to make way for Constable who has now scored in his last three Oxford appearances.
"We will respect that Aldershot have good players and got a good result up at Fleetwood, but we have to concentrate on ourselves and make sure that we are right," boss Chris Wilder told the club's official website. "We will have a few players back, Tony Capaldi, Peter Leven and Tommy Craddock, which is really good."
The club are waiting to discover the severity of the injuries Andy Whing and Jon-Paul Pittman picked up in the 3-3 FA Cup draw with Accrington.
The day will be tinged with sadness as the U's pay their respects to former player Mitchell Cole, with the players wearing special t-shirts in the warm-up and then everyone joining a minute's applause for the former United winger.
Wilder's side's 2-1 win over Northampton in their last npower League Two outing left them seven points above Aldershot in the first relegation place and the same amount behind the last play-off spot.