The runaway Premier League leaders turn their attention back towards Europe's top competition with a trip to Basel on Tuesday.
Kompany has already won every domestic honour available as City's long-serving captain but continental success has proved elusive.
This is the club's seventh Champions League campaign and they have only progressed beyond the last 16 once – losing a semi-final to eventual winners Real Madrid in 2016 – but the dominant nature of their performances under Pep Guardiola this season has many tipping City for glory.
"We lacked experience for sure," the 31-year-old centre-back said, reflecting upon City's early years in the Champions League at a pre-match news conference. "We've been caught out on occasions we shouldn't have.
"But things have changed. If there is a year, a moment when the club is ready to feel at home then it's now.
"I'm not going to say it's a matter of time, as some clubs never win it, but if every year we can go with this kind of confidence then if not this year or next year, eventually we'll get there. I'm sure of it.
"It's one thing for us to make that statement but [another thing] for us to go out and do it. In previous years we've felt how difficult it is.
"We are trying to break into a well-established order - Barcelona, Bayern, Real Madrid - any team who has tried it has failed.
"But first it's Basel, then getting to the stage where we can measure ourselves against these teams and feeling like we can beat them."
Training done pic.twitter.com/70OtXXE3Iz— Manchester City (@ManCity) February 12, 2018
City are heavy favourites heading into the tie but will be duly wary of a Basel side who beat their rivals Manchester United during the group stage and have enjoyed regular success against English sides at St Jakob-Park.
Wicky suggested his team face a tougher ask compared to when they took on Jose Mourinho's men earlier this season.
"They basically have no weaknesses," he told reporters. "Manchester City can change their game, they're flexible and can react to what their opponents do.
"They have quality, and their coach has shown his quality with Barcelona and Bayern too. They're an unbelievably strong team.
"We always try to prepare a plan, and we have one for tomorrow. Everything has to go perfectly for us in every single aspect.
"I don't think we'll be surprised by Manchester City tomorrow. Everyone knows how they play, and they'll have a lot of possession. They are incredibly quick in transitions.
"We have to be realistic, we're not going to have 50 or 60 per cent possession. We must be incredibly solid, very compact, very focused in every second of the game.
"When we have the ball, we have to have the courage to use it."