The England international has spoken out following Saturday's disappointing 3-1 defeat at West Ham which has left them down in eighth spot in the table - nine points adrift of Arsenal in the Europa League qualification place with seven games remaining.
It looks a tall order for the Baggies to make up the ground, but Foster feels victories in their remaining home matches could stand them in good stead.
"I think it will be a very big ask to qualify for Europe but we've got seven games left with four at home and three away," Foster told the club's official website.
"We know our home form has been very good so if we can get three wins from our four games we will be there or thereabouts. Our aim is to reach the mid-50s. We're on 44 now and if we can pick up another three or four wins it keeps us in the mix, at least."