After a first-half barrage, City finally managed to break the deadlock through David Silva.
Injuries to Benjamin Mendy gave the left-footer a chance to deputise for Fabian Delph for large parts of last season but he has failed to rack up the minutes this campaign following the Frenchman's return to fitness.
"After defeat to Lyon, we were under pressure". They made the game so hard but I think we controlled the game so well - especially on the counter attacks. "We have recovered well from Lyon and now it's in our hands".
In the first half hour, Riyad Mahrez could and perhaps should have scored twice, once after City had broken with breathtaking pace from their own half, before he then also set up David Silva to flick impudently against Shakhtar's post. When you arrive in the later stages we have to be more clinical.More news: Sensational Tsitsipas Makes Greek History In Stockholm, Claims Maiden Title
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The Premier League champions did not enjoy their last visit to Ukraine, having been beaten 2-1 in December previous year and will not want a repeat of that result.
It had been all City up to that point, with the Citizens boasting 90% possession at one stage and racking up a total of 15 goal attempts in a dominant first half.
"If they are here it is because they are ready to play", said the Spaniard. They played superbly in the first half.
'It was an fantastic result. "We missed a lot of clear chances".
Brazilian midfielder Fernandinho, meanwhile, who City signed from Shakhtar five years ago, said: 'We came here and to see so many familiar faces and friends; I'm so glad to come back here.
'I think we area playing better every game. we have to keep improving a little bit more but we're in a good way.