The Cottagers play Norwich at Carrow Road on Saturday, with the loser potentially dragged into the relegation mix.
"If you leave it until the end of the season you've always got a problem; you don't want that," Jol said. "What I always say is get to 35, 36 points as soon as possible, before the last couple of months of the season.
"We need four, five wins, and 40 points is the focus and target for us. I have been in this business longer than most managers and abroad you can say the bottom three at winter are likely to go down.
"But in England there are always surprises."
Fulham have three wins in eight games in 2013, are 13th, level on points with the 14th-placed Canaries, and, on 28 points, seven clear of the relegation zone.
But Jol is wary of Premier League precedent, with Birmingham relegated in the season when they won the Carling Cup and Blackpool going down after challenging for Europe earlier in the same 2010-11 campaign.
"With the amount of points we've got now, you go down," the Dutchman added. "You need fighting spirit in every game. This is the highest level and we want to get out of trouble as soon as possible, like seven, eight, nine other teams.
"You need very good spirit to do that and if you look at the other teams, they've certainly got that. If you look at the likes of Reading, winning games, Southampton, looking good, and, of course, Norwich are dragged into it.
"Everyone is still aware of the fact they need to win as soon as possible."