His goalkeeper Petr Cech saved a Clint Dempsey penalty in the last minute of last night's game with precious few chances.
But the draw means Chelsea are now 12 points behind leaders Manchester United with as many games to play.
And Ancelotti admits the FA Cup and the Champions League are Chelsea's only hopes of trophies this season.
He said, "Now (12 points adrift) is too much. Our aim is to play every game like we played tonight.
"Obviously it's very difficult to come back to fight for the title but we have a very important aim to reach until the end with the FA Cup.
"We want to come back quickly into the top four, and the Champions League returns next week."
"The most important thing is to finish in the top four. I think we will be able to do this if we play like we did tonight."
"I'm an optimist and there''s good reason to have confidence. I try to be objective every time. The football we showed tonight was good, and we have to continue it."
Chelsea striker Fernando Torres had another disappointing display after he was chosen to start ahead of Didier Drogba.
But Ancelotti believes his 50million pound striker he bought on transfer deadline day will prove to be worth the outlay.
And he defended his decision to play Torres alone, claiming Drogba merely needed a break, after the Italian manager insisting last week the pair can play together in the same starting line-up.
Ancelotti added: "Fernando played well. He used his ability to move. He had some opportunities in the first half and I took him out just to use Didier fresh and with power.
"That's the only reason I changed him. His performance was better than that against Liverpool. It was a normal rotation. We have a lot of games and I want to maintain the players fresh."
David Luiz was assured in his first start for Chelsea, until the last minute when he pushed Clint Dempsey for the penalty.
Fulham manager Mark Hughes, meanwhile, was aggrieved at ending with a draw after holding Chelsea at bay for much of the game.
And he criticised referee Mike Dean for failing to rule that the penalty be retaken, after he claimed Drogba encroached on Dempsey as he was going to take it.
Hughes said: "Given the circumstances at the end, it's disappointment. We came up against a strong Chelsea side who posed questions of us in the second half, and we had to be strong and resilient."
"We've been playing well of late and showed real character to dig in and create chances at the other end.
"The penalty should have been retaken anyway because Drogba was encroaching in the box. Mike Dean saw it: he was alongside Clint as he kicked it.
"Mike Dean saw that, so it should have been retaken. It''s a moot point, though, I suppose."