Mark Hughes' side claimed a 1-0 victory at home to Newcastle on Wednesday evening, a result which moved them up 12th in the table.
But Australia international Schwarzer insists Fulham cannot afford to relax until they have reached the 40-point mark.
"You're looking at points, not necessarily at the position you are in the table," said Schwarzer.
"The sooner we get to 40 points, the sooner we can start to look further up the table."
The keeper was a surprise starter against the Magpies, appearing just four days after the end of his country's Asian Cup campaign.
He immediately displaced Cottagers understudy David Stockdale, denting the 25-year-old's hopes of a maiden England call-up.
"It's always tough when you come in and you do well and then you get left out again," added Schwarzer.
"But it's also part of the learning process and you've got to see how you react."
Stockdale impressed while standing in for the absent Schwarzer, helping Fulham to four victories in six games and keeping three clean sheets.