City thrashed a 10-man Liverpool side 5-0 last Saturday before opening their Champions League campaign with a 4-0 rout of Feyenoord in Rotterdam.
City struggled against their top-six rivals last term and consequently failed to sustain a title challenge. On top of that they were unable to win away in the Champions League - the play-off round aside - and crashed out at the last-16 stage.
"Of course I am so satisfied," Guardiola said. "Of course, with 11 against 11 against Liverpool the game was equal. Eleven against 10 was much better but sometimes it's not easy to play 11 against 10, and we did it so well.
"People maybe thought it was easy to win in Feyenoord but going away in Europe is always so complicated. They didn't have one chance and that's so, so important.
"We did very good things but my feeling is the way we play we can improve (and it is about) trying to convince them that they are able to do that.
"Last season we were not able to win many games against the top five, top six in the Premier League. We didn't win one game away in the Champions League.
"First of all I start with that, to believe. To believe we can play good football and also that we can beat them and we can compete, even in the Champions League.
"That is the best I can offer or what I would like to give to my players, more than tactical issues."
Guardiola insists this does not mean his players lacked belief previously, but it is important to build on what they have.
He said: "I think every player believes but sometimes in a bad situation or moment we were not able to overcome the situation. You have to do that.
"You have to have a strong mentality so when you see the players they have the personality to play on the big stages."