The Potters picked up just five points from their first 13 Premier League games in 2013, but victories over QPR and Norwich have all-but guaranteed a sixth successive season of top-flight football.
With his side two points off 10th place, Pulis wants Stoke to continue their climb up the table with victory at Sunderland on Monday.
He 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."
Despite a poor second half to the season, Stoke could yet reach 49 points - their highest Premier League total - if they win their remaining games against the Black Cats, Tottenham and Southampton.
"Success for us, and always will be, is staying in the Premier League," stated Pulis.
"Anything else then is a bonus. We've got to maintain that focus. I don't think we can get above ourselves."
Pulis has come in for plenty of individual criticism in recent weeks, especially from supporters unhappy with the Potters' style of play.
Speculation about the Welshman's job has been rife, but he is keen to stay and it would be a surprise if chairman Peter Coates, with whom he has a very good relationship, opted to remove him.
Pulis said: "As a person you have to stay as level as you possibly can and, while the guns are firing and the arrows are flying past you, you've got to make sure you're strong enough to take them and move on.
"You have to accept you're going to get pats on the back and other people are going to kick you up the backside, that's part and parcel of management.
"It's one of the great countries in the world because everybody's allowed to say what they want to say. We've got to make sure we keep that part of our tradition. I understand how privileged I am."