Chelsea manager Frank Lampard refused to lay the blame of their first defeat in 18 matches at the feet of goalkeeper Edouard Mendy after his error led to Everton's match-winning penalty.
The Senegal international clumsily brought down Dominic Calvert-Lewin which allowed Gylfi Sigurdsson to score the decisive 22nd-minute spot-kick and inflict the club's third successive loss at Goodison Park.
It was his second mistake in two games as his error also led to a goal against Leeds last week but there were failings elsewhere with just 10 shots attempted in the game and not one on target after the 28th minute.
"He has been fantastic since he has been here and I don't think it was just clearly his mistake," said Lampard after coming off second-best against his former Chelsea manager.
"The mentality of the team to deal with second balls in the early part of the game was not good.
"This was a team that was well organised and who wanted to stop us playing and when you give them that head start it is difficult.
"I don't think we necessarily deserved to lose the game but if we are honest it was not the 'us' of recently.
"I think we could have got something out of the game, I wouldn't say we were unlucky but I don't think we were at our best tonight.
"We have been on a really good run and we knew what was coming with Everton physically and we didn't handle that well. We didn't show enough to break them down."
Necessity was the mother of invention for Everton boss Carlo Ancelotti as injuries meant he had to field a quartet of central defenders in his back four, while Sigurdsson was only playing due to playmaker James Rodriguez's calf problem.
But that actually worked in their favour as once they got ahead they were able to defend resolutely – his side had just 28 per cent possession – on their way to only a second victory in eight matches and first Premier League clean sheet since the opening day of the season.
"We needed this performance, we needed these points," he said.
"After a difficult period we were able to move on, we are now showing more consistency, at least tonight the performance was really good.
"You cannot win against Chelsea if you don't have a good performance.
"Defensively we were really good. We didn't concede opportunities, only set-pieces to shoot from outside the box but in (open) play we were really good because I think we were well organised with defenders and midfielders."
The match was the first which admitted fans to Goodison Park since March and the Italian felt that helped his side.
"It made a lot of difference, a totally different atmosphere. We had only 2,000 but the atmosphere was completely different.
"We are really happy for this. I hope all the crowd will be (back) soon as possible."