Shakhtar condemned Pep Guardiola's high-flying City to their first defeat in 29 matches courtesy of a 2-1 UEFA Champions League victory midweek.
Bernard and Ismaily were on target at the Metalist Stadium to send Shakhtar through to the last 16 and boss Paulo Fonseca kept his promise post-match, having said he would dress up as Zorro – a fictional masked vigilante – if the Ukrainian giants progressed to the knockout round.
"This is the most joyful news conference of my career," Fonseca said.
"I feel great joy. I think not only Shakhtar's supporters but all Ukrainians have to be proud of our team."
Shakhtar denied highly fancied Napoli a spot in the next round, finishing second and three points adrift of City.
"Tonight we played an almost ideal game. We were very disciplined in defence and broke through to attack very effectively," Fonseca said.
"It was very important to close up some particular zones for Manchester City where they are usually very dangerous. I think we did that well and they did not threaten as they normally would."