The Crystal Palace midfielder enjoyed a month at Priestfield between mid-September and mid-October, making seven starts during which the Gills won five and drew once.
Wright has not featured for Palace since returning to Selhurst Park and Allen, having made a move for his services ahead of last Thursday's 5pm deadline, saw his efforts thwarted merely by time constraints.
"David Wright is a very good player, we did try and get him but the paperwork didn't get done in time so we just have to deal with it, get on with it," Allen said.
"Like all disappointments you take them on the chin, deal with it, accept it and move to the next day.
"Of course I'm disappointed but we tried our best and the paperwork didn't get done in time."