City enjoyed the better of the clash at Kleanthis Vikelidis Stadium, with striker Edin Dzeko going close on several occasions for the visitors, but Mancini felt the playing surface had denied his side the chance to make their superiority pay.
He told ITV4: "I think we had control of the game but this pitch was difficult to play on, and I think if we had scored in the first half with Dzeko things may have changed. But they defended with nine or 10 men behind the ball so it was difficult."
But the Italian was pleased to see his side keep a clean sheet ahead of next week's second leg at Eastlands.
"It was better that we won this game, " he continued. "We tried but it was difficult as they defended well, but I think this is a good result.
"At Eastlands we will have a good pitch to play better football with the ball on the floor."