Chelsea, beaten at home by Liverpool last time out, had more than 20 attempts on goal but only four were on target as 50 million-pound striker Fernando Torres again lacked sharpness.
The result left Chelsea on 45 points, 12 behind leaders Manchester United with 12 matches remaining this season and two adrift of fourth-placed Tottenham Hotspur.
Manchester United are four points ahead of Arsenal with Manchester City third on 49. Chelsea still have to play United home and away but their chances of retaining the title look desperately slim.
"For the title this point is too little - we are quite far behind," Cech told Sky Sports.
"In the final third we missed a little bit and we were chasing the game at the end. It was up and down stuff so in the end, with the penalty, we are happy to get the point."
DIRE RECORD
Fulham had won their last five home league and cup games in a row but their record against Chelsea is dire with only one win against their neighbours since the 1970s.
They matched their big-money rivals for much of the game, however, and although Chelsea upped the tempo after the break they rarely troubled Fulham keeper Mark Schwarzer.
Torres looked odds-on to score in first-half stoppage-time when he ran on to a great long ball from fellow new boy David Luiz but he miscontrolled it, much to the delight of the home crowd.
Dider Drogba replaced the Spaniard for the last 20 minutes and though he looked lively he was unable to change things.
Chelsea were denied a strong penalty appeal when Florent Malouda was flattened by Brede Hangeland but the referee had little choice when Luis ruined an otherwise impressive display by mistiming an unnecessary challenge on Dempsey as the striker headed for the byline in the third minute of stoppage time.
Dempsey took the penalty but Cech saved well and the American's acrobatic attempt to latch on to the rebound flew wide.
