Manager Arsene Wenger hopes the spirit Arsenal showed in their brave defeat by AC Milan will see them back in the Champions League next season.
The Gunners beat Milan 3-0 in the second leg of their last 16 clash but lost 4-3 on aggregate.
A top-four Premier League place is now the aim for Wenger, who said: "It is a big disappointment for the players but the team have grown together.
"Hopefully from here we can finish the season in a strong way."
With 11 games to play, Arsenal sit fourth in the table after beating third-placed Tottenham and seventh-placed Liverpool in their last two league matches.
"We know there is no room for disappointment in the league," Wenger said. "For us every point is a battle and until the end of the season that is what is in front of us.
"Basically our target is possible because we are four points behind Tottenham. We have to go step by step. We have another big game on Monday night against Newcastle.
"For us, it is clear - we have to win our games."
Wenger's side can approach their task with renewed optimism after morale-boosting wins in their last three outings in all competitions.
For a while, their performance over Milan promised to bring them an unlikely quarter-final place, but Wenger was still grateful that his side salvaged some pride after the miserable defeat in the San Siro three weeks ago.
"We restored a good performance tonight and we are disappointed because we touched qualification," Wenger said.
"We had the chances and we didn't do it, but we were very close. I felt that we suffered a bit in the second half physically because we gave a lot at Liverpool.
"When we tired in midfield we had no options on the bench and the regret I have is there.
"The players put in a faultless performance, with fantastic spirit, and you can only congratulate the whole team.
"If you win 3-0 at home, you can only say well done to the players.
"You know that if you play 180 minutes and you miss 90, it is difficult at that level. We were very close."