The Potters secured victories over Queens Park Rangers and Norwich City, which lifted them from 16th in the table to 12th and has now put them eight points clear of Wigan Athletic, with three games to play.
Pulis told the club's official website: "We've got 40 points and good goal difference which is what we wanted. Now is the time to push on; we have to do that because mathematically we're still not safe.
"We need to get as many points as possible and it would be lovely to finish the season with a few more wins.
"If we can win two of our last three and get a draw we could end up in the top half of the Premier League, which would be a great season for us."
Stoke travel to the Stadium of Light on Monday to take on Sunderland.