Gordon Strachan last night greeted qualification for the knockout phase of the Champions League with a pledge to turn around his side's poor away record in Europe.

Celtic go into the draw for the last 16 of the tournament on December 18 despite being defeated in all three away matches in the group stages. The 1-0 defeat in the San Siro last night was not injurious to Celtic's hopes of progress as Benfica defeated Shakhtar Donetsk 2-1 in Ukraine. This left Celtic in second place despite falling to Filippo Inzaghi's goal that made the Italian the record goalscorer in European football with 63 goals.

"The most enjoyable part is the fact we are through," said Strachan afterwards. "I am still taking in the game itself. The coaching staff, chairman tell me it is a fantastic achievement but I'm still analysing the game. It was a tough group. After two games, Shakhtar were favourites to go though. For us to achieve nine points was terrific."

However, he insisted: "We must, if we are to do better, improve away from home. You must excuse me for dwelling on the negatives when there have been so many positives in the campaign so far. But we must do better away from home. I am desperate to sort that out."

He said that the next step for a side that regularly wins at home in the Champions League was to "be a force away from home in Europe".

The Celtic manager stressed that the next task was "to find out why we don't do well away from home in Europe and do something about it". Of the defeat in the San Siro, Strachan said that his team were carrying injuries in vital areas. He bemoaned the loss of his first choice full-backs and the subsequent crisis that forced him to employ four centre backs across the back four last night.

Strachan pointed out that against Milan, who play narrow in midfield, there is normally room for opposition full-backs to exploit but personnel changes made this difficult for Celtic.

He revealed, too, that Scott Brown was playing with a groin strain and that Scott McDonald had picked up an ankle injury in the warm-up. Brown will miss the first match of the knockout phase for picking up a yellow card for what his manager described as a "rash" challenge.

It was a tense night for Celtic supporters but Strachan said: "I was okay until Milan scored then I started looking about for help. Then I got the thumbs-up from the bench that things were going okay." He felt it was a "dead game", adding: "It was very hard to get momentum going. The pitch was dead, too."

Celtic, though, are very much alive in Europe. Who would Strachan want in the draw? "I've never really thought about it," he said. "For me personally, I'd like to try new arenas to play football. The players won't mind where they go. I would rather go somewhere rather than England."

Rangers need only to avoid defeat against Lyon next week at Ibrox to join Celtic in the last 16. Strachan was asked how he would react if his city rivals were successful. "I'd be delighted," he said. "We're through now. Everybody else can join us."

Carlo Ancelotti, the AC Milan coach, was pleased to go through as group winners. He said: "We controlled the game. We deserved to win. We had difficulties in the first half, but we had the right pace about our game in the second."

He said of Inzaghi's record: "We could see foresee it. He wanted the goal so much. He trained for it, he worked for it."

He praised Celtic for being "well organised, with good physical strength and good aerial play."

However, he stressed: "The fans are very important for Celtic, especially in the home matches."

He believed they could help Celtic to progress in the tournament. The coach also said that Dida missed an intriguing return against Celtic with a bout of influenza, He was questioned on why his side was so poor at home in Serie A - they have yet to win at the San Siro this season - and so good at home in the Champions league where they have won all three group matches. "In football,"" he said, "you don't always have a logical explanation."

This may be bad news for Strachan as he searches for the reason for his side's poor away record. However, it was the only bad news on a night when Celtic joined Milan in the last 16.