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The Blues conceded a late equaliser against Zenit St Petersburg on Wednesday, condemning them to second place in Group H behind Juventus.
Magomed Ozdoyev netted in the 94th minute to make it 3-3 after Romelu Lukaku had put the visitors in the lead.
And Ozdoyev's goal could prove problematic for Thomas Tuchel's side with Real Madrid and Bayern Munich two of the four teams they could play in the next round of the competition.
The Premier League side could also face a daunting tie against Erik ten Hag's free-scoring Ajax as well as defending French champions Lille.
Real topped Group D, winning five of their six group matches - including a 2-0 win over Inter Milan on Tuesday.
As for Bayern, they rampaged through Group E, collecting maximum points against Barcelona, Benfica and Dynamo Kiev.
Ajax also won every group stage match, scoring 20 goals in the process - with Sebastien Haller bagging 10 goals.
And Lille won Group G ahead of RB Salzburg, Sevilla and Wolfsburg.
Tuchel expressed his frustrations at his team's performance in Russia during his post-match press conference.
"I think that we had a very good first 15 minutes and then we stopped doing the things we did in the first 15 minutes," said the German boss.
"In the feeling, and this is my opinion, that this is okay what we are doing, that we are in charge, that we are the better team, but we are forgetting why we are the better team: because of the investment, the level of concentration, the level of physical investment was high enough to be the better team.
"And once this drops 5% or 10% - and it does - and once we start managing results and changing our behaviour from what the score is, we get punished at the moment.
"It happened to us in West Ham, it happened to us today.
"The reaction was again good, that shows me that it is not about what we can do - because we can step up and show a reaction when we concede goals - but once we have the lead we give it away again, like also today.
"So, the last six minutes we start playing balls back, we start not attacking in the same aggression and in the same hunger as before, and we got immediately punished now twice.
"It is for me about the level of investment, we have to do the things no matter what's on the scoresheet."
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