The Gunners finished the season in eighth place.
The Gunners beat Brighton 2-0 on the final day of the season as a second-half brace from Nicolas Pepe saw them win in front of fans at the Emirates Stadium.
But it was still not enough to secure European qualification as Arsenal had to settle for an eighth-placed finish for the second season in a row.
Despite that, Arteta is adamant the team have improved recently, ending the campaign with five consecutive league wins – their best run in the competition since October 2018.
“When I was with the team a few months ago and with them now, regardless of the results, we are in a much better place and will be in a much better place and can hopefully take the club where we want,” he said.
“It is frustrating because last season with 61 points we (would have finished) fifth, now we are eighth and that is the step that we have to identify.
“The level has gone so high so the only way to do it is to be much better next season and much more consistent and this is the challenge ahead of us.”
While qualification for the inaugural season of the Europa Conference League may not have saved a poor season, to lose out to rivals Tottenham due to a late Gareth Bale brace at Leicester would have hurt.
Some have suggested a season out of Europe for the first time in 25 years could be a good thing as Arteta looks to rebuild – but the Spaniard is not one of the them.
“It wasn’t in our hands. We tried to do our best, but it was not enough,” he said.
“This club deserves trophies and Champions League and we haven’t managed to do that in very challenging circumstances.
“We have tried to stick together and do our best, it’s not been enough. Now we have to be very critical of ourselves and prepare for next season in the best possible way.
Brighton came into the game having earned a surprise comeback victory over champions Manchester City in midweek and with their position in the top-flight already secure.
But with a number of players missing through injury, Seagulls head coach Graham Potter admitted his side were not at the races.
“They are important players,” he said of those absent from the game.
“If you have them you can rotate players that have put in such an effort and there are other options but it is life and it is how it is, we cant use that as an excuse.
“We did our best but we just weren’t good enough today.
“The boys kept going, I think they all did and I can’t criticise them for that, sometimes you have to be honest and say we weren’t at our level but not through the want of trying.
“We have had a tough week, a tough season and maybe today was a step too far for us.
“We weren’t good enough ourselves to maintain attacks long enough. We didn’t do enough to win the game so the result is a fair one.”