City crashed to a 2-0 defeat in the first leg of their Europa League last-16 tie as goals from former Chelsea striker Andriy Shevchenko and Oleh Gusev either side of half-time handed the Ukrainians a useful advantage.
Mancini was critical of City's defending with goalkeeper Joe Hart culpable for the first and Micah Richards for the second.
The Italian boss said: "I think that 2-0 is not a good result but at Eastlands it will be a different game.
"Tonight we played a good game. The difference was the goals we conceded. Usually we don't concede goals like this - we are more professional. We conceded two stupid goals. They played on the counter, so I'm frustrated.
"We didn't mark well for the first goal, the second goal the same. We were four or five metres from the opponent. When you mark in the box you should be near."
City rarely threatened as an attacking force after a bright start in freezing conditions and failed to live up to their billing as tournament favourites.
Mancini, however, is convinced they can keep their European campaign going and make the quarter-finals of the competition.
He said: "I think that we had some problems and I hope that it can improve with the strikers for the return match.
"If the strikers improve and the defenders pay attention maybe we have a chance to go through.
"Dynamo Kiev were fresher than us tonight. A few of us in the championship have played (recently) every three days."
Meanwhile, Mancini revealed that Balotelli was left suffering from an unexplained allergy.
The Italian was over a minute late coming out for the second half and eventually replaced in the 57th minute following a booking after complaining of feeling unwell.
Mancini added: "Mario had an allergy - I don't know what. His face was swollen - I don't know why.
"He wanted to play in the second half but he had this problem 10 seconds before coming out.
"I came out a minute before the players and I didn't see Mario.
"He then said he could play but his face was swollen."
It is understood Balotelli, who arrived from Inter Milan for £24million in the summer, is allergic to certain types of grass.
