The Blues took the lead twice in the pulsating stalemate through goals from Joao Felix and a well-taken penalty kick from Kai Havertz.
However, Sean Dyche’s dogged Toffees would not lie down as Abdoulaye Doucoure and Ellis Simms rescued an all-important point for the relegation-threatened side in west London.
Speaking after the game, Potter praised his team’s performance but rued their below-par defending that allowed Everton a route back into the game twice.
“We’re disappointed because we dropped points – we wanted to win,” Potter told ChelseaTV in his post-match interview.
“I think the intention of the team was positive – we did lots of things well, scored a good goal, then got a penalty.
“But ultimately we haven’t defended a couple of actions well enough, and that’s cost us a point in a largely positive team performance, but when you don’t win at home, we’re frustrated.”
Despite the disappointing result, Potter believes the team’s performance represents a step in the right direction.
“We have to treat every game like an opportunity to learn, develop and try to win – that’s where we are,” Potter added.
“A lot to play for when we come back from the break. We need to use the break well and then hope for an exciting April.”
The draw at the Bridge ended the Blues’ three-game winning streak this month but, on the plus side, it extends their unbeaten run to four games in all competitions.
Calls for Potter’s sacking have cooled, and while the Blues were undone by some poor defending, results like these are enough to get fans agitated again.
The Englishman will be hopeful that one negative result does not turn into two when club football returns after the international break, but Chelsea have some tough games coming up.
The Blues will begin their post-break run of fixtures by welcoming Aston Villa to the Bridge, before hosting top-four hopefuls Liverpool three days later.
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