The Cottagers moved to 10th spot on the table thanks to Saturday’s 2-2 draw at Sunderland but when asked if the players would start looking up the table, Schwarzer was erring on the side of caution.
“Not until you are mathematically safe do you stop looking over your shoulder,” he told the club’s official website.
“We’ve still got a lot of games to play and still got a lot of fixtures in the next couple of weeks which are away from home as well so they are going to be very difficult games and we need to make sure we pick up points along the way.
“The results mostly went our way today but you can’t keep relying on other results to go your way, you need to pick up points yourself and that’s what we are focusing on.”
Fulham find themselves sitting seven points underneath eighth and ninth-placed Swansea City and West Bromwich Albion whilst sharing the 33-point landmark with Stoke City and West Ham United with ten league matches remaining.