The News Agency of Nigeria (NAN) reports that City, who suffered their first defeat of the season in any competition, finished top with 15 points, three more than Shakhtar.
They also finished nine ahead of third-placed Napoli who dropped into the Europa League after a 2-1 defeat at bottom team Feyenoord.
A City side missing several regular starters was on the back foot in the first half as Bernard rifled a superb shot into the top corner in the 26th minute before Ismaily added the second in front of a full house in Kharkiv.
Substitute Sergio Aguero netted a stoppage-time penalty for City after Gabriel Jesus was tripped but coach Pep Guardiola had little to cheer about on his milestone 100th Champions League appearance as manager.
Meanwhile, Ronaldo set another Champions League record on Wednesday by scoring in Real Madrid’s 3-2 win over Borussia Dortmund and becoming the first player to net in all six group games.
Ronaldo doubled the lead for Real in their final Group H match against Dortmund at the Bernabeu with a curling shot into the top corner from the edge of the area in the 12th minute.
Ronaldo leads the scoring charts in the Champions League for the sixth season running with nine goals and is the top marksman in the competition’s history with 114 strikes, 17 more than nearest challenger Lionel Messi.
In other UEFA Champions League matches also played on Wednesday, Vincent Aboubakar struck two first-half goals to spearhead Porto’s emphatic 5-2 win over Monaco at the Dragao Stadium.
The victory ensured that Porto sealed their place in the knockout stages of the Champions League.
Also, Brazilian Philippe Coutinho struck a hat-trick as Liverpool crushed Spartak Moscow 7-0 to move into the knockout stages of the Champions League as Group E winners.
Liverpool manager Jurgen Klopp fielded an attacking line-up of Sadio Mane, Roberto Firmino and Mohamed Salah , with Coutinho playing behind them, and it was simply too much for the Russians to handle. (Reuters/NAN)