The hosts were relentless in their pressure during a first half in which they created a succession of chances but failed to punish Sean Dyche's side, before twice surrendering the lead as their three-game winning run ended.
Ellis Simms ran through a weak challenge from Kalidou Koulibaly in the 89th minute to side-foot Everton level and steal a point, after goals from Joao Felix and a penalty from Kai Havertz looked to have won it despite a leveller from Abdoulaye Doucoure.
Chelsea, increasingly fluid in their build-up play following their January spending spree, were again lacking a killer instinct inside the box as Everton were let off the hook repeatedly when the hosts poured forward.
It left them vulnerable to a late sucker punch, and it duly arrived when 22-year-old Ellis burst through to score his first goal for his side and boost their Premier League survival hopes.
"We're really disappointed because we've dropped two points at home," said Potter. "You saw the intention of the team, there was a lot of positive things in the performance. But ultimately we haven't defended well enough. To concede two goals means it's not so easy to win the game. That's the disappointing thing.
"Credit Everton, they do what they do well. They use their physicality, they use set-pieces, they ask you a question. But most of the game we controlled well, as well as you can at this level.
"Ultimately the first goal is really disappointing from a set-piece perspective, we spoke about that before the game. The second goal we haven't attacked well enough and expose ourselves to a big space to defend and haven't done it well enough.
"When you look at how much we put into the game and how much we tried to attack, to be cheap with the goals we concede is frustrating."
The game was memorable for possibly the best performance yet in a Chelsea shirt from Felix, whose threat with the ball at his feet caused problems that even Dyche's typically well-drilled defence struggled to handle.
His goal, the first he has scored at Stamford Bridge, was angled home brilliantly after Michael Keane had failed to deal with Ben Chilwell's cross.
He was the victim of some tough tackling from Everton who sought to contain him with brute force, including a particularly cynical challenge from James Tarkowski that the defender was fortunate to evade punishment for.
"Joao played a really good game," said Potter. "I thought he mixed his game up well, he ran in behind, he linked up, dropped in, he combined well with Kai and with Christian (Pulisic) and Enzo. Really happy with his performance.
"There's always going to be physicality in the Premier League, you expect that. It's up to the referees to see all the incidents. But he's adapting and learning all the time.
"Results-wise it's a step back. But performance-wise it's a step forward. I think there was a lot of good in the game. I thought we attacked well; Joao, Kai, Pulisic were positive in the first half. Reece (James) and Chilwell used the width well, Enzo I thought was creative in midfield.
"Individual performances were positive. The team's intention was good. But the feeling is frustration because we've dropped points."