No Palace side has ever spent longer than a single season in the Premier League and Pulis, who boasts a record of never being relegated during his managerial career, believes there is still plenty of work to be done if he is to become the first man to steer the south London side to safety.
"It was three points against Chelsea but that is gone now," he said.
"The most important thing is to focus on the next game, which is probably going to be more difficult
The lads can take a lot from the way they played last weekend but that goes out the window when we kick-off on Saturday.
"All that counts now is the Cardiff game
We need to make sure we put in enough performances like last weekend to get us over the line.
"If people think it is all over and done with after the Chelsea game it isn't, we have still got to get the points because everyone down there is fighting
We have go focus on getting the points as quickly as we can."
With Cardiff - promoted alongside Palace last season - also fighting for their lives, Pulis is anticipating a challenge when he takes his side to south Wales and reckons even a third away win of the campaign would not mean top-flight football is guaranteed for next season.
"Cardiff will want to drag us back into it," he said.
"They have got some good players - It will be a very difficult game for us but we have known that all season
We have been the underdogs all season and that will continue, irrespective of where we are in the table.
"Three points this weekend will not see us safe, we have to keep going until we are mathematically safe.
"We have played well [away from home] this season without getting results
We have got four games left away from home and we have got to pick up points in those games
People will still write us off but that is not a problem with me."
As the lowest-scoring side in the division with just 20 goals, finding the back of the net has proved to be the Eagles' main problem for much of the season.
On-loan Stoke striker Cameron Jerome has only one goal, scored in the reverse fixture against Cardiff, while Glenn Murray has just returned from a long-term knee injury.
Summer signing Marouane Chamakh has six goals to his name and the former Arsenal man has drawn plaudits for his effort since Pulis took charge at Selhurst Park.
The 30-year-old Morocco international is back in training after missing four games with a hamstring problem and Pulis is hoping to be able to give Chamakh a run out in Cardiff.
"Chamakh has trained all week and he looks ready to go," the Welshman confirmed.
"Whether we start him or whether he is on the bench, we will have to wait and see
It is a decision we will make closer to the game.
"He has been outstanding for us, he has been the player that gives us something different
Chamakh is important to us
He has got tremendous technical ability and can open the door for us."
Source: PA