For many, Bravo struggled in City's derby win.
But he insisted: "Good, good - comfortable.
"We have a team here that has personality, we are improving day by day and the matches that we want to win are these, against our rivals, and for that reason I am happy.
"I am happy with my first week, with the work I have done.
"We played well against a very big team and a team that was very strong and they kept putting the ball in the air to try and complicate things, but we survived."
City teammate Nolito also insisted: "I think Claudio Bravo is a magnificent goalkeeper, a spectacular goalkeeper.
"We are very happy that he is here with us. We are very relaxed with him and that's it.
"It's a special day for him because making your debut in a derby like this is not easy.
"And I thought he played well and I am happy he signed for us, so congratulations to him. I am happy that he is with us and he played well."