Celtic out as Milan and Ajax heap on misery There was little surprise when Neil Lennon identified failings in both attack and defence as the principal reasons why Celtic were unable to secure the win required against AC Milan last night, as the worst of all possible scenarios unfolded for his side. Needing a win to keep alive hopes of a Champions League last 16 berth, Celtic fell to a heavy home defeat. Goals from Kaka, Cristian Zapata and Mario Balotelli extinguished Celtic's hopes before the hour mark. Even though the Italian visitors took the lead through Kaka after only 12 minutes, Celtic had already passed up opportunities to score. But their main chance to get back into the match came just after half-time when Virgil van Dijk shot straight at the goalkeeper from the edge of the six-yard box after a free-kick had been played back in by Joe Ledley. Elsewhere things did not go to plan either, with Ajax defeating Barcelona in Amsterdam after taking a two goal lead before half-time. Although Barcelona pulled a goal back, the 2-1 result means Celtic do not even have the consolation prize of Europa League football to aim for in their last Group H match at the Nou Camp in two weeks" time. Lennon was frustrated by the lapses that were evident throughout the 90 minutes - Milan's first two goals came from corners, for example. However, he also stressed that Celtic's performances in the group stage, where they have scored only two goals and conceded eight, underlined the deficiencies in a squad stripped of two main assets during the summer. Gary Hooper and Victor Wanyama both left for the English Premier League and Lennon has struggled to replace them. If we want to look to the future and continue to play in the Champions League then we have to improve the squad we have now and we have to improve our recruitment for next year," said Lennon. It's never a forgone conclusion that you're going to be in the Champions League. We do have some money and we want to spend it, preferably in the January window. But it's not as if we didn't try to spend it in the summer. We had three or four targets in mind but they fell through for various reasons. January is a difficult period to bring players in but we need to do that with next summer and the qualification play-offs in mind. Lennon described Celtic as being "contributors to their own downfall" last night. He rued the extent to which injuries had impacted on their performances in Europe this season. Beram Kayal was forced off last night with a hamstring injury in the first half. "I don't think we were outplayed," said Lennon. Big moments in the game changed the course of the game and the psychology of the game. Milan took their chances when they came along. We had opportunities through Kayal, Mulgrew, Van Dijk and Forrest and snatched at them. That was the difference. We had already lost some big players - Adam Matthews, Scott Brown, Nir Biton - and losing Kayal as well tonight, that's three midfielders out of five. When your squad is not as big as some other squads it does tend to bite you. It was a bracing night for Celtic, who might also face punishment from Uefa for a banner briefly unveiled by fans in a corner of the stadium where the Green Brigade gathers before kick-off, and which made a comparison between William Wallace and IRA hunger striker Bobby Sands. But Lennon pledged to do everything possible to return to this stage again next season. He has often stressed that merely reaching the group stage this season was an achievement in itself, particularly after the departures of Hooper and Wanyama during the summer. "We will do everything we can to come back and compete again next year -that's the target," he said, I think tonight is symptomatic of our campaign - we missed good chances and I am really disappointed with the two goals we conceded from corners, I take a lot of pride in that and that's the first time for a long time that someone has scored directly from a header against us. The Virgil [van Dijk] chance was a good one and, at 1-1, the game could have gone either way. And then we go and concede again from a corner and that's the most disappointing aspect, as were the opportunities we missed. We knew when the draw was made how difficult it was going to be. But we competed and we have competed again tonight. Lennon did not expect going out of Europe in November to impact significantly on the rest of the season, nor on the Scottish Cup clash with Hearts at Tynecastle this weekend. There will maybe a little bit of a hangover, but that is something I want to avoid. We are going well domestically and we have a big game on Sunday and that's a good one to get our teeth into. There are players here who are playing very well and there are players here who need some more game time and improve us as a squad. Asked about James Forrest's frame of mind after he had started the day of a big Champions League clash by being charged with alleged indecency after an incident on Ayshire, Lennon said: "James has a hamstring problem and has missed the last couple of weeks. I thought he played well tonight but we took him off as a precaution with future games in mind. I need James to have a consistent run of games because we haven't had that luxury for quite a while now. It's been a question of trying to manage him. Asked again whether his experience earlier in the day had made him consider leaving him out, he shook his head. AC Milan manager Massimiliano Allegri praised his side for their defending and asked for the match to be put in context. Despite their troubled start to the Serie A season, this victory he said was historic. We played well tonight, but we also played well v Napoli, where we lost. But praise the players. This was a very important victory. Put it into context - Milan have only won once here before, and that was in a European Cup quarter final in 1969. It was not an easy victory. We nullified Cetic. They created three or four good chances but on the whole we defended well.