Nicolas Pepe's delightful free kick looked like giving Arsenal the points but Lewis Dunk equalised for the hosts before Neal Maupay struck five minutes into stoppage time.
Defeat left Arsenal in ninth spot in the table with 40 points from 30 games, six behind fifth-placed Manchester United.
"I am very frustrated," Arteta said.
"It is unacceptable the way we lost the game. We like competing and I know we have a young squad but still, we threw the game away. We had to put it to bed earlier.
Before the Premier League was suspended because of the pandemic, Arsenal were on a three-game winning run in the league that had revived their hopes of qualifying for Europe.
However, after losing to Manchester City on Wednesday and now Brighton, it looks a tough task.
"We need to try to lift the players. There's a lot of things that they've done really well, but we don't compete," Arteta said. "At this level you can't give the goals that we give away.
"It's impossible. I know that we are a very, very young team but in the Premier League if you make two mistakes like this, you lost two goals. We can't accept that."
Arsenal also lost keeper Bernd Leno to a knee injury after he tangled with Maupay just before halftime. Arsenal's players reacted angrily at the French forward who hit back at suggestions he was reckless.
"Some of their players need to learn what is humilty -- especially one of them. He was talking all game, he was saying bad things," Maupay said. "I don't want to say because I could be in trouble. I just said that this is what happens when you talk too much on the pitch.
"I just went for the ball. I am that type of player -- I don't want to stop until the referee blows the whistle."
Arteta stopped short of criticising him.
"I always believe players never have the intention to hurt anybody and I'm sure he didn't have the intention to do that."
It was a massive three points for Brighton who gave themselves a five-point cushion over third-from-bottom Bournemouth in the relegation battle.
Traore inspires Wolves at West Ham
Adama Traore came off the bench to inspire Wolverhampton Wanderers to a 2-0 win at West Ham United on Saturday -- a significant result at both ends of the Premier League table.
The quicksilver Spanish winger was perhaps surprisingly left on the bench for 64 minutes but his introduction enlivened an otherwise humdrum encounter at an empty London Stadium.
Traore's surging run and sublime cross was perfect for Raul Jimenez to head powerfully home in the 73rd minute.
Traore was then involved again in the move which ended with fellow substitute Pedro Neto firing home a sensational left-footed volley to seal the win that lifted Wolves into sixth place, level on 46 points with fifth-placed Manchester United.
Defeat for West Ham, their fourth in their last five Premier League games, left them in 17th spot, ahead of Bournemouth, who play Crystal Palace later on Saturday, on goal difference.
West Ham worked hard to match Wolves but struggled to create much apart from a glorious early chance for Pablo Fornals who lashed a shot wildly high and wide.
The home side must have feared the arrival of Traore from the bench and so it proved as he provided the spark to earn Wolves an important win in their quest for Europe.
West Ham's left back Aaron Cresswell is no slouch but he could get nowhere near Traore who powered past him before clipping over a cross for Mexican Jimenez to chalk up his 14th goal of the season, nine of them assisted by Traore.
Traore then showed some fancy footwork before passing to Matt Doherty whose cross was dispatched in style by Neto.
No wonder Traore was named man of the match for his 25-minute cameo appearance.
"It's about using the substitutes at the right moments," Wolves manager Nuno Espirito Santo told Sky Sports.
"We needed this win to feel that we are really back. We will never get used to playing without fans. Let's hope and pray we get a vaccine or something so we can be together again."
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