The Blues looked like they were heading for a win until Hector Bellerin’s strike in the 87th minute.
Chelsea head coach Frank Lampard has bemoaned the "basic errors" which cost his side two points on Tuesday night.
The Blues were twice pegged back by 10-man Arsenal at Stamford Bridge.
Jorginho broke the deadlock in the 28th minute from the penalty spot after David Luiz was shown a red card for his foul on Tammy Abraham in the penalty box.
Gabriel Martinelli cancelled out the opener in the 68th minute with a cool finish after a long run from his own half, but Cesar Azpilicueta restored the lead for Chelsea in the final 10 minutes with a tap-in as he converted Callum Hudson-Odoi's cross.
The Blues looked to be heading for a win until Hector Bellerin’s strike in the 87th minute (Arsenal’s second shot in the game) made it 2-2.
"I am disappointed given the situation of the game. We completely deserved to go 1-0 up. For a little bit after that we were getting used to them with 10 men," Lampard told BT Sport.
"We created enough in the second half, it was the same story for us that we don't finish our chances and we made errors to give them two goals on the break. It probably shows where we are at. These sort of things don't lie.
"We work hard but basic errors when you should control the game can end up losing you points.
"It's not the slip from N'Golo [Kante], that can happen, it's that they get away from the edge of our box. That's a moment sleeping, people should know their jobs.
"And then the last goal, so easy to cut back. It's the sort of goal you see over the park, a right-back that moves it slowly onto his left foot and rolls it in the far corner. That can't happen."