"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."
West Brom have seven games left to play in their Premier League campaign.