Arsenal manager Arsene Wenger hopes the disappointment of elimination from the UEFA Champions League can spur his team to a top four finish following their agonising near-miss against AC Milan. The Gunners bowed out of Europe on Tuesday after narrowly failing to overturn a 4-0 first leg deficit against the Serie A leaders, with a rousing 3-0 win, not enough to prevent the Italians squeezing through 4-3 on aggregate. For 45 minutes, Arsenal seemed poised to pull off one of the greatest comebacks in the history of European football, with Laurent Koscielny, Tomas Rosicky and Robin van Persie putting them 3-0 up at half-time. But a more disciplined defensive effort from Milan in the second half, and a rare squandered chance from the prolific Van Persie, saw Arsenal fail to score the fourth goal that would have levelled the tie. Arsenal\'s shattered players could not hide their disappointment following a pulsating encounter - but Wenger has urged them to bounce back from the hurt of elimination as they retrain their sights on the Premier League. \"We are on a good run in the league and it will be difficult - I don\'t deny that, because tonight was a big disappointment fort the players,\" Wenger said. \"But the team has grown well together that hopefully from here we can finish the season strongly because there is no room for disappointment. Every point is a battle until the end of the season and that is what is in front of us. Successive league victories over Tottenham and Liverpool have cemented Arsenal\'s grip on fourth place in the table, and they are now only four points adrift of Spurs having trailed them by 10 points less than two weeks ago. Wenger was cautious about the prospect of Arsenal reeling in Spurs over the closing months of the league season. \"Our target is possible because we are four points behind Tottenham, but we have to go step by step because we have another big game on Monday against Newcastle,\" Wenger told reporters. \"We take it game by game and we need to win our games and look at the results of teams like Tottenham to catch them up, but for us, it\'s clear - we have to win our games.\" Wenger meanwhile had few complaints about Arsenal\'s elimination, which he attributed to a poor performance in the first leg that left his side with too much ground to make up. \"We are disappointed because we touched qualification, we had the chances, and although we didn\'t do it, we were very close,\" Wenger said. \"In the second half it was harder to keep the ball than in the first half and when we tired in midfield, we had no opportunities on the bench - and the regret I have tonight is there - because the players gave a faultless performance with a fantastic spirit and you can only congratulate the whole team. \"We have played so many matches in the Champions League and never lost 4-0 away before, at Real Madrid and Barcelona, and we played against better teams, but in the first leg our performance was poor.\" \"If you win 3-0 at home you can only say well done to the players. But if you play 180 minutes and are missing for 90, well it\'s difficult at that level. But we were very close.\" Milan coach Massimiliano Allegri meanwhile said his team would have to improve if they were to advance beyond the quarter-finals. \"Right now, although we lost I am very happy, I am delighted we\'ve qualified and that was the main objective, although we have to play better than that,\" Allegri said. \"All that really mattered was the result and that we got through to the next stage. Today was in some ways the match of the season for us because now we are among the best eight teams in Europe.\"