I know things might change, but I don't think there's any need to swim against the current if it's too hard to be true. Copenhagen must accept the fact that they have failed in the Champions League this season even though they still have 2 matches in the round of 16, that's because Manchester City is their opponent. The same thing about Lazio and Leipzig who are each playing against Real Madrid and Bayern Munich.
They didn't fail but they can't progress anymore, they didn't fail because they have passed the group stage and playing the knockout stages. I didn't know the club before but as they played in the knockout stage, I know them now and so will many other people watching the champions league. Copenhagen can't beat Manchester city, Manchester city will be too strong for them. Manchester city will want to defend their title therefore they'll be seeing every team as an opponent to win with perfect record. Manchester city will sore many goals against Copenhagen. From the first leg of the round of 16, Copenhagen will already know they can't progress to the quarter finals. Manchester city always get easy teams at the round of 16 and it's because they always top their groups.