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"We let the opponent get back into the game," he said. "First, we didn't do much right in the second half but then we gained more control after Shaqiri entered the pitch.
"It's important we are first of the group. Maybe the loss is good because it shows the Champions League is very complicated. The Bundesliga is hard, too. It is hard to convey that if you always win. Maybe it is necessary to lose. Even if it is not that important. The players gave everything, Manchester City is a great team."
“Someone said yesterday that our priority was the Arsenal game but this was a very important game for us, too,” Pellegrini said. "It was a very important game because we played very badly at the Etihad Stadium against Bayern and we wanted to show that we are a good team.
"We played very bad for the first 16 minutes but when we started keeping the ball, we played the way this team knows how to do and we played the same as Bayern. I had some doubts about their goals being offside – I think on one of them their player has come back from an offside position. After we scored, when you keep the ball and you have trust and confidence in what you do, all of the players started to play well.”
"We got to the top of the group and that's what we did want," he said. "We knew we'd qualified before tonight's game, so if we'd lost it would have been important because we wanted to win it, but in the same breath the win helps us, helps improve our form a little bit.
"We hadn't played that well tonight, especially in the first 30 minutes, they had two or three opportunities, but I thought just before half time we started to get a little bit better, had one or two chances ourselves and second half I thought we were much better."
Despite City's best efforts, Bayern finish top of the group due to their head-to-head record against the English side. The Manchester team have to settle for second spot, while Viktoria Plzen claim third spot after their 2-1 win against CSKA Moscow, who finish bottom.
PSG had already claimed first place in the group before tonight, and they will be joined in the knockout stages by Olympiakos after the Greeks pipped Benfica to second spot due to their 3-1 win against Anderlecht. The Portuguese side finish third and have to settle for a place in the Europa League.
Real Madrid had already claimed top spot before today, but the group has still not quite been settled due to the Galatasaray-Juventus game being postponed due to snow. The replay of that match will take place tomorrow, with the Italians needing just a point to take second, while the Turkish side need to win. Whoever misses out will take third spot.
Victory for United means they top the group, while Leverkusen's win means they take second spot. Shakhtar will have to settle for the Europa League after being leapfrogged by the German side.
"I think we had to show a bit more desire tonight, a bit more belief in ourselves and in the performance, I thought we did that eventually," he said.
"We got to grips with it in the second half. First half was a bit shaky and a bit tentative but I thought we got to grips with it and created a lot more chances."
It's all over around Europe now so let's have a glance at tonight's results...
Manchester United 1-0 Shakhtar Donetsk
Real Sociedad 0-1 Bayer Leverkusen
Copenhagen 0-2 Real Madrid
Galatasaray p-p Juventus
Benfica 2-1 Paris Saint-Germain
Olympiakos 3-1 Anderlecht
Bayern Munich 2-3 Manchester City
Viktoria Plzen 2-1 CSKA Moscow
"After a somewhat difficult first half, Manchester United weathered the storm and, eventually, scored the all important goal through Phil Jones. Qualification for the knockout stages was secure prior to kick off, but the win ensures David Moyes leads United to top spot in Group A in his first time in the competition proper, and puts a slightly more rosy complexion on what has been a difficult last seven days."
Anderlecht, who were already down to ten men, have had two more sent off in N'Sakala and Proto. CSKA, meanwhile, are now down to ten men after having Wernbloom sent off. Madness!
The full-time whistles have blown in both City and United's games. City's 3-2 win against Bayern means they will have to settle for second spot in Group D, while United's win means they top Group A.
Pellegrini has made another change as City look to go on and score another. But, strangely, it is a rather defensive switch as Rodwell comes on for Dzeko. The Chilean obviously not too fussed about finishing top of the group it seems.
As it stands, United will be finishing top of Group A, but City will be finishing second in Group D. Still a few more minutes that could change all that, however.
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