City saw numerous waves of attack break up as a stubborn Brighton defence held out until the 70th minute when Dale Stephens' error in possession opened up space for Sergio Aguero to score.
Lewis Dunk's own-goal soon after gave City a comfortable margin of victory in an opening weekend that has seen Arsenal concede three at home to Leicester, Liverpool draw at Watford and champions Chelsea lose to Burnley.
Failing to win against the likes of Leicester, Stoke and Middlesbrough contributed to City's title charge fizzling out last term and, having once again been installed as pre-season favourites, Kompany believes new-found patience and grit make Pep Guardiola's side a greater threat.
The skipper told BT Sport : "We had to be patient first half, they were defending really well. They were organised and you could see they had a clear game plan, but we've got quality and eventually it made the difference.
"Talking about attacking options - we know it in training of course because we have to face [Aguero] every day.
"But the season is going to be long and today was an improvement on a lot of things we did last season.
"We had a five-minute spell where we were under pressure. We put our bodies in, we made some important tackles and eventually we got the goal because we were patient.
"Ultimately [we have] a lot of positive things to take from this game and we kind of built on the pre-season we had."
Guardiola plumped for a 3-5-2 system, with Aguero and Gabriel Jesus paired in attack, while Kyle Walker and Danilo provided wide support from wing-back.
The former Tottenham man was named man-of-the match for a persistent display on the right flank and was happy to begin his City career on a winning note.
"We knew what their game plan was going to be - to sit back and defend," he added.
"Probably a draw would have been good result for them but we needed a win. Opening day of season, it's always good to get off to a good start so we're happy."
On the change between life under Guardiola and Mauricio Pochettino, he added: "It's different. They both have their certain way of managing and how they want to play but it's positive.
"I'm enjoying working with the lads, everyone's been welcoming. Being at one club for eight, nine years it's a big change for me but I'm enjoying my football.
"I'm enjoying my football and it's better to play with a smile on your face."