A clinical finish from Sergio Aguero and a Lewis Dunk own goal secured victory on the south coast despite stubborn resistance from the Seagulls.
City were not always at their brilliant, fluent best, but with a flurry of goals, thrills and surprises around the grounds on matchweek one, a regulation road win was just the tonic for the travelling fans.
Guardiola said: "We saw all the games in the Premier League today and yesterday, how complicated it was for everybody. We knew that Brighton are a newly-promoted side, with enthusiasm, also with their crowd.
"But we had chances in the first minutes and after the game was quieter, it's not easy to attack 10 guys in the box.
"We controlled the counter-attacks, we conceded just one chance in 90 minutes away from home and that's not easy in the Premier League.
"We are so satisfied for the first game, the way we played. It was quite similar level to pre-season in terms of working without the ball, and we are going to improve."
"I want to say thank you to the Club, for the next four, five years we have young players with huge talent," he said.
"Last season with Leroy and Gundogan, this season with Bernardo, Danilo, Mendy and with Kyle - they are young enough to play four, five years. So big congratulations to all people working with City, we are a strong Club."
Guardiola added: "We were stable, we have to try to improve, but what's important in the first game is to win."