City came back from a goal down twice against Liverpool at Anfield to earn a 2-2 draw, but Mancini slammed his defence after shipping another double.
The Premier League champions conceded twice on the final day of last season, and have done in all three games this campaign, including the Community Shield clash against Chelsea. Mancini called for this run to end, while also complaining about the free-kick awarded to Liverpool which led to the Reds' second goal.
"I think that it's time we finished conceding two goals every game", he told Sky Sports.
"Before this [happens] we need to work. Today the two goals were set-pieces, the second goal wasn't a free-kick, it was like the goal we conceded here last year, but we do need to improve."
The 47-year-old did praise his team's character though, saying he was pleased with the manner in which his players fought back despite ending up with what he feels is a disappointing result.
"I'm disappointed because when you don't win you are always disappointed," he continued.
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"But you know that at Anfield it is difficult to play and in the end if you go and take one point like today, go two times down and score two goals, yeah, we showed good character."
City lined up in a changed formation with three at the back and five in midfield but reverted back to their more familiar shape during the game and Mancini feels his side need more time to get used to the new system.
He added: "I think we need more time, for 30 minutes we always had the ball."
"Playing in their half we had four or five chances to score but then after we conceded from the corner, something needed to change."
Finally, the Italian confirmed the club will work hard as we enter the final week of the transfer window.
"We have five days, we should work really hard."