Arsenal appeared set to go in at half-time deservedly ahead following Nicolas Pepe's opener, only for David Luiz to concede a penalty following a challenge on Willian Jose.
The Brazilian centre-back was shown a red card by referee Craig Pawson following a VAR check, though Arteta insisted he could not see any contact after studying replays of the incident.
Ruben Neves converted from the spot before Joao Moutinho's long-range strike put the hosts ahead shortly after the break, with any hopes of a fightback disappearing for Arsenal when goalkeeper Bernd Leno was given his marching orders for handling the ball outside the area.
For Arteta, though, it was the David Luiz call that left him frustrated, particularly after his side had played so well up until that crucial moment in the contest.
"First of all, I have to say that I'm proud of my team, the way we played and the way we dominated the first half," Arteta told the media.
"We should have been 3-0 or 4-0 up. We didn't do that, though, and we put ourselves in a really difficult position by conceding the goal and going a man down.
"I have seen the replay 10 times from five different angles and I cannot see any contact. I would like to see if VAR has a different angle. I'm expecting to see something and I'm not seeing anything.
"We were really animated at half-time because we really wanted to win the game. The boys were so convinced to go out there and have a real go.
"We didn't concede any chances but Moutinho scores a worldie and it's 2-1. Then, when Bernd comes out and hits the ball with his hand, we're down to nine men and almost impossible to win the game."
Since making his league debut for Arsenal in August 2019, David Luiz has picked up three red cards and conceded six penalties, more than any other player in the competition in both categories.
Arteta - who has seen his team shown nine Premier League red cards since taking charge, six more than any other top-flight team - admitted the result was tough to take.
"The way we lost the game really hurts. It's painful," he said.
"I have to take the positives as well, which is the way we played against this team that is very difficult to attack, the amount of chances we created. But we leave the ground and have zero points and have lost two important players.
"It's hard enough to win football games in this league. There's nothing we can change. It was a big decision, if they got it right and can justify they got it right, I'll put my hand up and apologise.
"The only thing I'm saying is that I’m sitting here and I cannot see any contact. That's really, really frustrating, because it's a big, big moment in the game."
Asked if Arsenal may issue an appeal against the red card for David Luiz, Arteta replied: "Where I’m standing now, I'd say yes – let's go straight away. But I don't know, we will have to speak to the legal team at the club and decide if it is the best thing."
Runar Alex Runarsson came on to take over from Leno in goal, with recent recruit Mat Ryan ruled out with a muscle issue. Arteta revealed he is hopeful the Australia international can be fit in time for Saturday's trip to Aston Villa.