Arsenal, who finished a disappointing eighth last season, sit fourth in the Premier League standings, two points ahead of London rivals Tottenham Hotspur with five games to play.
Arsenal last played in the Champions League in 2016-17 when they reached the round of 16.
"Qualifying for the Champions League would be an important achievement, and something very necessary and powerful for the club moving forward," Arteta told Sky Sports on Friday.
Asked if he was ready for criticism should they fall short in their bid, Arteta replied, "That's part of the job and the expectation that we have here is to not only be in the Champions League but also win trophies every single year."
Since arriving as the manager in 2019, Arteta has led Arsenal to the FA Cup and the Community Shield.
Arteta, whose team travel to West Ham United on Sunday, said the club will look to strengthen the squad in the summer as they aim to win major trophies again.
"We want to make the squad stronger, the starting 11 stronger, the specificity and the personality of our players stronger, and that's what we are going to be seeking to do," he said.
"It will depend on many factors... How many players are back from their loans, with the commitments we still have with them, our financial position in relation to where we finish, and the clubs' demands when we want to buy players or sell players.
"There are a lot of question marks there, but this is football... The good thing is that the plan is clear, but the plan is just the plan until you start to work through that plan."