Mancini said: "We need to pay attention in the defensive phase because they were two stupid goals.
"We played a good game but made two big mistakes for the two goals."
City will face a huge task to turn the tie around on 17 March at Eastlands against a confident and well organised Dynamo side.
A disjointed City created few chances at the Valeriy Lobanovskiy Stadium, with David Silva missing the best opportunity when he failed to direct Pablo Zabaleta's scuffed cross towards goal from close range.
Mancini added: "Kiev are a good team. The right result might have been 2-1.
When you play in the Europa League, you can't concede goals like this Roberto Mancini "We had control of the game. They played counter-attack. I'm frustrated because we conceded two goals."
City struggled to cope with the Ukrainian outfit's front quartet of Shevchenko, Andriy Yarmolenko, Artem Milevskiy and Roman Ermenko as Dynamo showed they were a step up in class from Aris Salonika, who City disposed of easily in the previous round.
"When you play in the Europa League, you can't concede goals like this," Mancini explained.
City, who had won four of their last five games, will need rediscover their form in front of goal ahead of a crucial period for Mancini's side.
The Eatslands outfit are still battling for success on three fronts this season with Champions League qualification a priority.
They sit in third place in the Premier League, seven points behind leaders Manchester United.
Meanwhile, they have the chance of silverware in the FA Cup where they face Reading in the sixth round on Sunday.