Despite admitting that Gus Poyet has "done a fantastic job" since taking charge of Sunderland in October, Allardyce believes that the team may find it hard to stay in the top flight.
"In the position they are in now, the games are running out. They have games in hand due to their fantastic run to the League Cup final and when you are catching those games up at this stage of the season, it is difficult and puts that added bit of pressure on them," he told West Ham's official website.
"Everybody goes around saying 'If you win this game or that game you are going to be safe' but points in the bag are more important than games in hand at this stage of the season. I think it puts a little extra pressure on them, knowing they need to win those games to get out of the bottom three and out of trouble. That may tell in the end.
"Gus Poyet has done a fantastic job since he's been there and the effort from their players and him have been great in terms of trying to get out of the position he started from. It just goes to show how difficult it is to get out of that situation after a bad start."
West Ham and Sunderland drew 0-0 when the sides met at Upton Park in December.