City has now lost on Wearside for a third season in a row, although it had several chances throughout the game, forcing Black Cats keeper Simon Mignolet into a string of impressive saves.
The defeat, coupled with Manchester United's dramatic 4-3 win over Newcastle, leaves Mancini's side seven points adrift in the title race and the Italian was bewildered at his strikeforce.
"Next year we won't come. We won't spend the money to come here but in the end we won the title [last season]," He told BBC Sport.
"We didn't deserve to lose, we dominated this game, I don't know how it's possible that we didn't win this game, but every year it is the same.
"I'm frustrated at this because it's impossible that our strikers don't score but we have this problem, we don't score enough to win the game. This is a big problem at the moment."
Pablo Zabaleta appeared to be fouled in the build-up to Adam Johnson's goal and Mancini criticized referee Kevin Friend and his officiating team for their overall performance.
"Maybe Zabaleta deserved a red card," the Italian scolded. "I don't think the referee and the linesmen had a good performance today."