Scolari claimed it was "incredible" the American midfielder was allowed space inside Chelsea's area to score his second goal of the game from a corner and cancel out Frank Lampard's second-half double.

Dempsey had put Fulham ahead after 10 minutes with a neat far-post finish when Simon Davies' free-kick was allowed to bounce in the Chelsea box.

Scolari left the field in conversation with goalkeeper Petr Cech and admitted Chelsea had paid the price for their mistakes.

"We lost two points today," said Scolari, whose Chelsea side enter 2009 three points behind Barclays Premier League leaders Liverpool.

"We made two mistakes with our marking and conceded two goals. I think they had one more chance - we had 10 chances and scored two goals.

"We have been very good with corner kicks and free-kicks this season but not today. Before the game every player knows who to mark. It is my job now to look and see what happened. It is my dressing room. I need to look at it.

"After the first goal we tried to make sure it didn't happen again but we made another mistake.

"I asked Petr what happened because one player was free in the middle of the area in the last minute. It is incredible. Petr is the captain for this area."

Had Chelsea stationed a defender on Cech's right-hand post, Dempsey's header may have been cleared off the line - but Scolari does not believe in the tactic.

"Posts do not score goals, players score goals," he said.

Chelsea lost ground on Liverpool, who ended 2008 with a 5-1 thrashing of Newcastle, and will be overtaken by Manchester United if the champions win their three games in hand.

Scolari continued: "The championship is not finished today. It will be finished in the last two or three games. It is normal in England. The Premier League is difficult."

Dempsey's late header was a fitting way for Fulham to celebrate the first anniversary of Roy Hodgson's appointment as manager.

Twelve months ago, Hodgson took over a club that seemed doomed to relegation. Not only did Fulham survive but this season they have beaten Arsenal and taken points off both Liverpool and Chelsea.

Today's result extended their unbeaten run to nine games and Hodgson said: "It's been one of the best managerial years of my career, if not the best. I'm immensely satisfied with what we've achieved in 2008.

"It was a remarkable achievement for the players to show the spirit and the character they showed to come back and keep the unbeaten run going.

"We didn't start the second half well and as a result of their good pressure they scored two goals. After we went 2-1 down we did find our feet again a little bit, we did play more football and as a result we were able to put their goal under more pressure."