The Toffees were desperately unlucky not to come away from Stamford Bridge with all three points have initially led 2-0 and then 3-2 going into stoppage time.
But a late - offside - equaliser means Everton have slipped into the bottom half of the table after failing to win for four Premier League matches.
Many fans and pundits tipped the Goodison Park outfit for a Champions League tilt in this most open of Premier League seasons.
But that now looks unlikely as they trail fourth-placed Tottenham Hotspur by 10 points as we approach the business end of the campaign.
While their style of football and attacking verve has won Roberto Martinez's side plenty of plaudits, there remains deficiencies as a defensive unit.
'I think it's the manager's style'
And their former manager David Moyes has delivered his verdict on Everton and Martinez as a guest on BBC's Match of the Day.
"I think when they went 2-0 up, there were signs, they lost two goals in I think two or three minutes after that and they've got a great position, to be 2-0 up at Chelsea what a great result," Moyes told MOTD.
"It went away from them.
"I think it's the manger's style (playing open football), and he's playing very well, the team's playing very well but I think there has got to be times in the game when you shut up shop and you try and get a result."
Everton need a middle ground between Martinez and Moyes
The Toffees have been entertaining fans with some exhilarating football under Martinez.
Many would argue it is the kind of football that would not have been witnessed under Moyes, who was known for his more pragmatic style.
But where Martinez is lacking in the defensive department and organising his side to keep things tight, Moyes excelled.
It is finding a balance between those two styles which will be key to Everton's future success.
But after spending big on the likes of Romelu Lukaku and Gerrard Deulofeu and handing major contracts to key players like Ross Berkley and John Stones the pressure is on Martinez to achieve success.
Silverware would be a good way to do that with the club taking a 2-1 lead into the second leg of their Capital One Cup semi-final against Manchester City next week.