A 1-0 loss at Sixfields left Chris Wilder's men six points behind seventh-placed Rotherham having played two games more than the Millers.
And Constable concedes the pressure is on the players to prove they are worthy of a place in Wilder's squad for 2013/14.
"Everybody wants to play and prove that they are good enough to be here," he told the Oxford Mail.
"If we don't make the play-offs, the situation changes - the gaffer is going to need to improve the squad and bring players in and it might mean that if you're not doing it you're not involved and you might not be part of his plans for the following season.
"Everybody, whether they are under contract or not, is playing for their futures."