Arteta's side crashed to a 3-1 aggregate defeat after losing 2-1 in the second leg at the Parc des Princes.
It was a painful loss for the Gunners, who created numerous chances in the early stages, only to be denied by a series of superb saves from Gianluigi Donnarumma.
Goals from Fabian Ruiz and Achraf Hakimi put PSG in control and although Bukayo Saka reduced the deficit, it was too late to spark a sensational fightback.
PSG will meet Inter Milan in the final, while Arsenal face up to a trophy drought that has now extended to five years.
Arteta responded to the loss in combative fashion, claiming Arsenal were as good as PSG and were unlucky not to have beaten the French champions.
"When you look at the two games their best player on the pitch has been the goalkeeper, he has been the difference for them in the tie," Arteta said.
"I'm very proud of the players. We were very close, much closer than the result showed but unfortunately we are out.
"After 20 minutes it should have been 3-0. We were very close and for long periods of both games we were much better than them but we are not there (in the final) and that has to hurt."
Not for the first time this season, Arsenal paid the price for a lack of cutting edge and untimely defensive mistakes.
And even Arteta had to concede the north Londoners were punished for their failings in both penalty areas.
"If we want to win this competition we have to realise that. There are certain things that are on us. You shouldn't just be understanding we are out. That is not the way I look at it," he said.
"I don't think there has been a better team in the competition.
"This competition is about the boxes, and in the boxes are the strikers and the goalkeeper. He (Donnarumma) was the best player in both games."
Having failed in their bid to win the Champions League for the first time, the Gunners are still waiting for their first silverware since the 2020 FA Cup.
Injuries to key players played a major role in their failure to push Liverpool in the Premier League title race.
And Arteta insisted his wounded side's gallant display against PSG -- who had already knocked Liverpool and Aston Villa out of the Champions League this season -- gave him hope for the future.
"The players deserve a lot of credit for what they are doing in the context of the situation and the amount of injuries, probably the worst state you could arrive here as a team," he said.
"To come here with a different context and still do that, it gives me a lot of positives for the future but tonight I am very upset."