Runaway leaders Liverpool hold a five point advantage over second-placed Arsenal and have two games in hand to come, starting with Sunday's clash against struggling Manchester United at Anfield.
Shorn of many of their most potent attacking weapons, Arteta's men led at half-time thanks to 17-year-old Ethan Nwaneri's strike.
But two vital points slipped away when William Saliba was harshly punished for a clash of heads with Joao Pedro and the Brazilian slotted home the resulting spot-kick.
"We are really disappointed with the decision that leads to the goal because I have never seen something like this in my life," said Arteta. "He (Saliba) touches the ball as well."
With talisman Bukayo Saka out for the next two months with a hamstring injury, Arsenal's attacking options were further depleted by illness.
Kai Havertz failed to even make the matchday squad for the second consecutive game, while captain Martin Odegaard and Gabriel Martinelli were only fit enough for appearances as second-half substitutes.
Nwaneri was the beneficiary with a second consecutive start and showed why he is one of the Premier League's rising stars with a clinical finish for the opening goal.
The teenager still had plenty to do as he raced onto Mikel Merino's ball over the top but his pace took him beyond the Brighton defence before firing low into the far corner on 16 minutes.
But even he then had to replaced by Martinelli at half-time after suffering a muscle injury.
"We gave the ball away and we didn’t do the simple things well enough to be really on top of the game and have the dominance we required," added Arteta.
"We did a lot of things not to the standard with the ball. So we didn't get any momentum, we never got set in areas that after we could generate chances."
Arsenal lacked any penetration without their quartet of attacking stars to build on their lead.
Merino had the one big opportunity to double the Gunners' advantage early in the second period when he skewed wide from Declan Rice's free-kick.
Moments later the visitors were rocked by a controversial call that could have huge ramifications for the title race.
There was the slightest touch from Saliba's head onto Joao Pedro's but the Brighton forward went down clutching his face and got the reward of a spot-kick.
The Seagulls captain for the day, in the absence of Lewis Dunk, confidently stroked home the penalty to level.
Arteta responded immediately by summoning Odegaard from the bench.
However, it was Brighton who looked the most likely winners in the closing stages.
Yakuba Minteh wasted a great chance to end their now eight-game winless run when his shot across goal evaded both Yasin Ayari and Kaoru Mitoma and slid wide of the far post.
"It should be more than a point," said Brighton boss Fabian Hurzeler.
"We came back but we were not clean enough in the final third. We had big chances."
A point is enough to edge Brighton back into 10th.
