City make their Champions League debut at home to Napoli on Wednesday on the back of four wins out of four in the Premier League.
Their latest success, an easy 3-0 win over Wigan at Eastlands on Saturday was inspired by a hat-trick from Sergio Aguero.
But Mancini believes there is much more to come from his expensively-assembled side, and insists there is room for improvement.
"I think we had about 15 chances in the first half and only scored one goal and this is a problem because every moment in a game can change," said the City manager.
"Maybe the game was closed after the second goal, but next time we have to close the game in the first half.
"The whole team played very well, but we need to improve. We've started the season very well, but the season will be long and if we are to stay on top for a long time we need to improve."
Mancini also claimed his players are suffering from fatigue ahead of their Champions League debut - despite a recent 13-day international break.
He said some were suffering as they had played two games for their countries during the break.
"The players are so tired," revealed the Italian. "Some of them have played two games for their national team and need to recover over the next three days."
Aguero proved he is in excellent form ahead of Napoli's visit after taking his tally to six goals in four games since joining from Atletico Madrid for £38 million last month.
But Mancini was reluctant to single out the Argentina international after an easy win which ended Wigan's unbeaten seven-match run.
He said Carlos Tevez, who started for the first time this season after being stripped of the captaincy, was just as impressive.
"Sergio played very well but so too did all my players. I enjoy watching it because I like it when we play football very well," added Mancini.
"Carlos (Tevez) is not 100 per cent fit at this moment, but I am happy for him because for me he played very well. He linked well with Sergio.
"It was important for him to start and play well. Maybe in two or three days time he will be 100 per cent."
On the challenge posed by Napoli, Mancini said: "It will be a hard game. It will be the first time that we have played in the Champions League. It will be an exciting night. Napoli are a good team and the first group game is always difficult."
Wigan manager Roberto Martinez believes City can flourish against Europe's elite after witnessing the likes of Aguero, Tevez and David Silva destroy his side.
"What is quite clear is that they do not play in straight lines," said the Spaniard. "They have got a fantastic football awareness and they are wonderful players to watch.
"The understanding between Silva, Aguero and Tevez - that is something special. That is why football becomes so creative and so unpredictable and so difficult to stop.
"I think Barcelona, three years ago, when they started with Frank Rijkaard, they had little flashes like Manchester City showed.
"Three years down the line, you'll be able to compare to a side like Barcelona. Nobody can be compared to Barcelona yet. You have to win many titles, you have to play many games together.
"But what is quite clear is that the ingredients of this Manchester City have got the capability to achieve anything in world football."
Source: AFP
Source: AFP