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Manchester City manager Manuel Pellegrini apologised on Friday for the miscalculation that may have cost his side top spot in their Champions League group.
City came from two goals down to win 3-2 at Bayern Munich in their final Group D match on Tuesday, but they would have overtaken the reigning champions at the top of the pool if they had scored another goal.
Having won 3-1 in the reverse fixture, Bayern finished above Pellegrini's side thanks to their superior head-to-head record, meaning City are likely to be handed a daunting tie when the draw for the round of 16 is made on Monday.
Speaking immediately after the game in Munich, Pellegrini gave the impression that he thought City needed to win by three goals to top the group, and he has now admitted that he got his sums wrong.
"It shouldn't have been happening, but it is very easy why it happened," he explained at a press conference.
"Before the match I knew we had to win 3-0 because we needed one goal more than they scored here.
"After, when they score the first goal, I continued (thinking) that 3-1 was not enough because they had a better goal difference, so I continued (thinking) that we had to win by three goals; 3-0 or 4-1.
"After, when they scored the second goal, I didn't continue thinking about what happened if we scored four goals.
"That was my mistake, because not many teams score four goals against Bayern Munich. I tried to think better about how to arrange the game that we were losing 2-0.
"First of all, I recognise absolutely my mistake, but I don't have any guilty conscience about what we did because we always tried to score the fourth goal."
He added: "I apologise for me and the team that we couldn't score four goals against Bayern Munich."
Pellegrini, whose side host leaders Arsenal in the Premier League on Saturday, played down the significance of City's failure to secure first place in the group and said qualification was all that mattered.
"That is the most important thing. I am not afraid of who we are going to play in the round of 16," he said.
"I don't believe some teams are weaker than the other teams. I believe the 16 best teams in Europe are all exactly the same for us.
"I think the trust the team has after beating Bayern Munich in their own stadium, that is much much more important than being first in the group."