The Eagles have won just twice away from home heading into Saturday's game at the Stadium of Light against Sunderland.
Palace are 16th, three points clear of second-bottom Sunderland.
"From when I came in to where we are now, we have done fantastically well," Pulis said.
"I have a great group. What we have to do is to step up another level to get us over the line."
Palace suffered a 1-0 home defeat to Southampton last weekend and Pulis remains frustrated by some of the refereeing decisions that went against his club.
"Against Southampton, in the first 20 minutes we had two great opportunities where the linesmen flagged," he said.
"I've been on to the Referees' Association and the linesmen should get those decisions right because the two were onside.
"(Glenn) Murray was through on goal and had just the goalkeeper to beat.
"In the second half when (Southampton defender Jose) Fonte brings down (Palace's Yannick) Bolasie, that is a sending off.
"In Premier League games, you need things to go for you and they never did. If Murray had been allowed to go on and score, it would have been a different game."
Pulis does not expect anything to come easy this weekend.
"It will a tough game, it always is," he said.
"They are a big club, the fourth or fifth best supported in the Premier League. It's absolutely fantastic for us to go to the Stadium of Light and play against a great football club."
Sunderland were eliminated in the quarter finals of the FA Cup after a 3-0 loss at Hull City last weekend.
They have had their own share of problems, winning just six league games all season, including three at home.
"I'm surprised to see Sunderland where they are," Pulis said.
"I thought they would be higher up. You look at the squad, they have some very good players.
"(Sunderland coach Gus) Poyet is a good manager.
"He did a very good job at Brighton and he's gone on to take Sunderland to a (Capital One) Cup final and came very close to going to a (FA) Cup semi-final.
"I'm sure they will be up for this game. We have to go there and stand up and fight our corner."
It has not helped Pulis that their leading scorer Marouane Chamakh is still sidelined with a hamstring injury.
"We missed Chamakh on Saturday," Pulis said.
"Murray did really well against Southampton and it would have been great to have played Chamakh with Murray but that's not possible.
"The important thing is that we get back to what we've been doing well and fingers cross, over the next 10 games, we get the breaks that my players deserve.
"We have to stick together, make sure we get through the last 10 games and give it the best we possibly can."
The Eagles have the worst striking force in the Premier League when playing away from home, having found the net just six times in 13 away games.
"The one real disappointment is in set plays," Pulis said. "We should be scoring more from set plays."