Adam told the club's official website: "We have to step up to the mark now because we have just six games to go.
"There isn't time for us to wait and hope things happen, we have to go out and get the points we need.
"It is worrying, but we won't talk about relegation. We are an established Premier League team and we are still looking upwards. We need to get points on the board, though, there is no doubt about that."
Stoke face Manchester United in the Premier League next Sunday.