The Gunners looked set to break their three-match winless streak in the league as Gabriel Martinelli scored from a superb cross by the returning Martin Odegaard in the 60th minute.
However, Arteta's men were pegged back just 10 minutes later when Pedro Neto unleashed from range before Leandro Trossard failed to convert William Saliba's pass from close range in the final seconds of the match.
Trossard's late miss saw Arteta collapse onto the pitch, while the Spaniard was also left pondering a fresh double injury blow after both Declan Rice and Bukayo Saka were unable to complete the match. Arteta revealed the England duo are a doubt for the forthcoming international break.
Odegaard's first start since September provided Arsenal with a timely boost, but their season has been derailed by a series of injuries and suspensions.
TrendingSpeaking after the score draw at Stamford Bridge, which marked the first time Arsenal have gone four matches without a win in the top flight since April 2023, he said: "There's nothing that we can do about that.
"What I'm praying for is that after the international break we have the team fully physically equipped, that they are available and that they are fit, because, it's been a nightmare for eight weeks.
"Doubt after doubt, issue after issue, not only with the ones that are not able to play, but with the ones who are able to play.
"I am disappointed with the result because I think we deserved more. After scoring the first goal, I'm very disappointed with how we conceded their goal. That's nowhere near the standards of our defensive habits, how we allowed it.
"The moment you give space and time, you're going to get punished, so that's not bad luck. Then the team showed its teeth. We created three big chances. Unfortunately, we weren't able to put the ball in the net, but we deserved to win it."
Rice, who was a doubt heading into the fixture with a broken toe, was replaced after 71 minutes, while Saka was also withdrawn in the second period following a robust tackle by Marc Cucurella.
"It doesn't look good, because for two players of that importance to tell you they cannot continue in the game, obviously it's not good news," added Arteta.
Asked if he expects them to be available for England's Nations League matches against Greece and the Republic of Ireland, Arteta replied: "Well, two players that just came off, I don't know whether to expect them to be fit, because if not they don't come off."
' Paul Merson:
"It's hard for Arsenal. They have a bullseye on their back. They are a big team and everybody wants to beat them.
"I find that their confidence is a little bit low at the moment. It wasn't free-flowing against Chelsea and when your confidence goes, not everyone wants the ball. When they are in full flow, everybody is moving. It's like the red arrows.
"Against Chelsea, when Partey, Rice and Odegaard had the ball, there wasn't a lot of options. There aren't five or six passes on.
"Arsenal have to go on a run now. They have to find some consistency. They can do it, they can reel off five or six wins on the spin and they are going to have to do it to get back in the title mix.
"They will not be far away, [it was] a good performance in Milan, although they did not really look like scoring and it is a hard place to go and they were completely comfortable. Raya did not make any world-class saves.
"So it is a start, but as Arteta says, he has to get the players fit now, they have to go on a run and make sure it comes down to six points before it goes up to 12 points - if it gets to 12, it is goodnight."