After picking up only five points from their first 13 games in 2013, Stoke appeared to be in major danger of slipping into the bottom three, but back-to-back wins over QPR and Norwich have settled nerves.
The Potters now sit 12th, eight points clear of 18th-placed Wigan and only two points adrift of a top-10 place, ahead of Monday's trip to Sunderland.
Pulis said: "We've got 40 points and a good goal difference, which is what we wanted. Now it's the time to push on.
"We have to get more points. Mathematically we're still not safe. It would be lovely to finish the season with a few more wins.
"The worry is the longer (the bad run) goes on, you get dragged into it.
"Winning breeds confidence and confidence is a massive factor in professional sport, individually and collectively. We'll go up to Sunderland on Monday, we know it will be a tough game, and we'll give it our best shot."
There has been plenty of doom and gloom in the Potteries in recent months but wins from their remaining games against Sunderland, Tottenham and Southampton would see Stoke reach 49 points, their highest Premier League total.
A first top-10 finish is also within sight, but Pulis' mantra throughout the club's time in the league has revolved around staying on an even keel, and that will not change.
He said: "If we win the remaining three I think that will be the record number of points that we've returned in the Premier League, but that's the Premier League, there's thin lines between success and failure."
- Sports & Recreation