Guardiola’s men received widespread praise for a lot of their play, particularly in the first half, in Saturday’s 2-1 derby defeat of Manchester United at Old Trafford.
That success in the Premier League was City’s sixth victory in succession since Guardiola took charge but the Spaniard insists his there is still much to prove.
Speaking ahead of tonight’s clash with Borussia Monchengladbach, he said: “We are now after four games in the Premier League but I would like to tell this brilliant audience and our fans, we are first in the Premier League but the way we have played until now, it will not be enough to win the Premier League.
“We have to improve to win the Premier League. Of course we are so happy for the results, for the numbers, for the way we are playing after two months but it is not enough to win the Premier League or to achieve big targets in the Champions League.”
Last week Guardiola played down much of the hype surrounding the eagerly-anticipated clash against United and the potential psychological impact of victory.
He maintains that stance even though the manner in which City took the game to their rivals, who have also been tipped to challenge for honours this term, sent out a strong message to opponents.
“We made good things and bad things and we have to improve for the future. Of course we are happy but that is all. It is just three points.”
One negative aspect for City has been the criticism levelled at goalkeeper Claudio Bravo after a difficult debut.
The Chilean, signed from Barcelona for £17m (€20m) last month, made the mistake while led to United’s goal and had several other anxious moments.
Guardiola, who controversially axed England number one Joe Hart, was again forced to defend his man.
He said: “He is so strong. I saw the game [again] yesterday we played against United to realise the things we made good and which things we have to improve.
“I saw the goal and what happened in the the three or four actions after when he received the ball. He showed huge personality. That is what I tried to say after the game. I was convinced before the game and after seeing it again it is the same.
“But I am going to tell you something. Claudio Bravo, Willy [Caballero]. and Angus [Gunn] are going to make mistakes in the future, they are not going to save all the goals and opponents are going to score goals. I am pretty sure of that.”
Guardiola has now turned his attention to the Champions League and the visit Monchengladbach. In a group which includes favourites Barcelona, City are keen to get off to a good start.
Guardiola said: “They are a brave team [with a] brave coach — one of the best teams in Europe. They have a lot of quality. The draw was difficult for us, Barcelona was there, especially with Gladbach.”