The Gunners have drawn their last four Premier League games to slip down to 10th in the table, 10 points adrift of fourth-placed Chelsea.
However, they now have three successive home matches – against Newcastle, Everton and West Ham – which offers them the chance to put pressure on the teams above them.
Manager Arteta said: "The next two or three weeks is going to dictate how close we are going to be in the last four or five weeks of the season to challenge for the European spots or not."
Arsenal have lost just once in nine games since Arteta took charge in December, but have won only three of those games.
Just one of those wins has come in the Premier League, at home to Manchester United on January 1, and Arteta has stressed the importance of stringing some victories together.
He said: "I think winning takes you to winning the next game and the confidence related to that is huge, which in football the mental aspect is more important than anything else.
"So when you are doubting about yourself and your ability to win games, obviously the confidence affects, but that's part of something that we need to go over and improve, and the moment that comes I think that will generate naturally another dynamic."
Asked what it will take to change the results, Arteta said: "I think you have to do a lot of things. You have to do things in training, the messages you are sending to the players, the messages they send by themselves, it's a lot of things."
If Arsenal are to mount a genuine push for a Champions League berth then they will need several of their star players to hit top form.
One of the men who could have a big influence but has yet to show his best this season is Nicolas Pepe.
The Ivory Coast winger joined Arsenal in the summer for a club-record £72million but he has scored only five times in 27 appearances this season, compared to 23 in 41 for Lille last term.
Arteta hopes the 24-year-old will soon start to show what he can do, but points out that Pepe would not be the first foreign player who needed time to adapt to the demands of English football.
Arteta said: "I hope that we can see (improvement) from now until the end of the season.
"But if you go through the list of top players that have joined this country, how disappointing they were for the first 10, 12 months and how incredible they were for the next five...
"I think we could have a massive list here because it's not easy to adapt to this league, but he's put in the effort and he's willing to do it, and it will come out."