The majority of the U's first-team squad are out of contract in the summer and Saturday's defeat to Northampton appears to have all but ended their slim hopes of a play-off place.
Despite being United's top scorer for the past four seasons, Constable admits that the pressure is on the entire squad.
"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 future."