City played against 10-man Stoke after defender Abdoulaye Faye was sent off in the 53rd minute.
Glenn Whelan sent Stoke in the lead while Gareth Barry grabbed an 85th-minute equaliser.
“It was a difficult game because in the first half the ball was almost always in the air – never on the pitch,” Mancini told Sky Sports.
“For us, that was difficult, and after that we played better against the 10 men.
“But, for me, we must play better. We needed to play more in the channels and not in the middle, which is better for them (to defend).”
“I’m disappointed because if you play 11 against 10 you must have more chances to score a goal, more chances to win the game,” added the City boss.
“This game was important and we should have won it because we played for 40 minutes with a player more.”