Having already secured their place in the last 16 after winning Group A, City had little to play for as they took on the crisis-hit German side behind closed doors at the RB Arena on Tuesday.
Yet after Kyle Walker was sent off for an act manager Pep Guardiola could not defend and Phil Foden and Nathan Ake were withdrawn through injuries, City were left to count the cost of an underwhelming 2-1 loss.
“Obviously everyone is disappointed because we didn’t get what we came for but we need to get our heads up and move on for the future,” said left-back Zinchenko.
“We need to take the best from this game and do our best. We are going to watch the game and analyse it and we need to react quickly and move on.”
Guardiola made seven changes from the side that beat Watford last weekend but still fielded a strong side.
Kevin De Bruyne was among those to return as the Belgian made his first start since his recent spell out with coronavirus. Foden and Jack Grealish featured as they continued their recent return from injuries but the former was withdrawn at half-time as a precaution after feeling a problem in the ankle.
Foden and Ake, who came off with a back issue late in the game, will now be assessed ahead of Saturday’s lunchtime Premier League clash with Wolves at the Etihad Stadium.
Despite the eerie atmosphere reminiscent of much of last season, both sides approached the game positively.
Yet it was Leipzig, who sacked manager Jesse Marsch last weekend and have had a Covid outbreak to contend with, who carried the greater threat.
They secured victory with goals in each half from Dominik Szoboszlai and Andre Silva. Riyad Mahrez pulled one back for City but Leipzig held on to claim third place in the group, and a Europa League spot, after Walker’s needless dismissal.
The England full-back was shown a straight red card eight minutes from time for a frustrated hack at the legs of Silva. Guardiola said the suspension that will follow “hurts” City for the next round.
“Of course, everyone is sad and disappointed for that,” said Zinchenko. “He is such an important player for our team and he is going to miss the first game in the next round, but even with that we need to be on top of the situation.
“Like I’ve said before, it is a good achievement to go through, especially in first place. We are looking for the Champions League draw and we need to prepare well.”
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