Carlo Ancelotti rued Everton's failure to match Fulham's "intensity" as the Blues missed the opportunity to close the gap on the sides above them in the Premier League table.
Manchester United's 1-1 draw at West Bromwich Albion meant the Blues could have climbed to fifth and within six points of Ole Gunnar Solskjaer's second-placed side with two games in hand.
However, a second-half Josh Maja double inflicted a first defeat in four on Ancelotti's charges, keeping them seventh.
Everton are two points behind Chelsea and West Ham United - both on 39 - with a game in hand. Liverpool, a point further ahead in fourth, have played twice more than the Toffees.
The Blues now face a crucial week in their season with leaders Manchester City set to visit on Wednesday night, ahead of a trip to Anfield next Saturday.
"Of course we are really disappointed because with a victory we could have climbed the table," said Ancelotti.
"Now we have two difficult games to play but I think we need to have hope because usually, in these kind of games, we play better.
"We have to have focus but in the difficult games usually we play well and I think we can do the same on Wednesday.
"The performance was not good enough and not what we expected because we knew it was an important game. But we knew also it would be difficult."
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GOMES ACCEPTS EVERTON 'MUST LEARN FROM MISTAKES'
Everton started second best against Fulham but came close to taking the lead when captain Seamus Coleman struck the post with a left-footed shot from the edge of the area on 34 minutes.
Substitute Joshua King later had the ball in the net but was denied a first Blues goal by an offside flag.
That was as close as Everton came and Ancelotti felt his side paid the price for the exertions of Wednesday's nine-goal epic against Tottenham Hotspur in the FA Cup, a 5-4 win that required extra-time.
Everton have now played seven games in 22 days and four in the last 12.
"I think we suffered because of the two hours against Tottenham," conceded Ancelotti. "We were not able to [match] the same intensity that Fulham put on the pitch, pressing a lot and putting pressure on our centre-backs.
"I think usually we have done well when we have played every three or four days. But two hours, I think that was a big effort and, physically, we didn't have the power that was necessary to match the intensity of Fulham.
"I think that was one of the aspects but not everything, because sometimes you have to say the opposition team played better than you and they deserved to win.
"I am surprised they are in the bottom three because they played well not only against us but against Liverpool and Manchester United, also. They are a team that has a clear idea and they deserved to win tonight."
Another blow to Evertonians was the sight of James Rodriguez limping off midway through the second half, though Ancelotti is hopeful of positive news on the Colombian.
He added that England duo Dominic Calvert-Lewin and Jordan Pickford will be assessed ahead of the visit of Pep Guardiola's City.
"[James] had a knock in training. I think it will not be serious," said Ancelotti.
"We are going to check tomorrow, like we have to check Dominic for the game on Wednesday, and also Allan and [Jordan] Pickford."