Mancini laments lack of cutting edge
Vicenzo Iaquinta scored with a deflected long-range effort as Juve had the better of the early stages, but City bounced back with a well-worked Adam Johnson goal before the break.
City then had more of the game in the second half, but it was Juve who came closest to finding a winner as Alessandro Del Piero's free-kick came back off the underside of the bar.
"Juve started the game well, especially in the opening 20 minutes, and scored the goal with Vincenzo Iaquinta," he told the Italian media.
"Then we started to improve and in the second half we maintained the initiative throughout. It's true we ran a few risks on the counter-attack, but we should be more incisive in the box."
Juve boss Luigi Del Neri was happy that City were unable to impose themselves on the game.
"We forced Manchester City to play badly and fully deserved the point this evening," he said. "It was a very strong Juve performance, because we never lost our desire to win right to the end and had some excellent opportunities for the victory.
"I am happy with this result, especially for those who said we'd lose tonight and concede a hatful of goals."
Johnson revealed his goal came as a result of work on the training ground.
"I've been working on it a bit in training, running across defenders," he said. "The manager wants me to do it more. It was a great pass by Yaya Toure. My first touch took it away from the goalkeeper and I thought I might need another..."
On the game, he added on Five: "It was hard. Italian sides obviously defend well but I think we were the better team. In the second half they were pegged in their own half for most of it. I think we should have won the game."