Man City have won 11 domestic trophies since the Abu Dhabi takeover in 2008, including four Premier League titles, but have only reached the Champions League semifinal once in that time.
On Saturday, they face French side Lyon in Lisbon in the quarterfinals and Walker said lifting the trophy for the first time in the club's history is the only way for City to announce themselves as a European powerhouse.
"I think if you had asked me this two years ago when I signed here, I would have probably said that the Premier League was the big one for me having not won it before I came here," Walker said.
"Now I have collected two of them and a number of others and this is the one that I want, and I can probably speak on behalf of the whole squad and Manchester City as well for what they need as a club to put them onto that next pedestal."
The 30-year-old is hoping City already hold an advantage over Lyon ahead of their last-eight clash because of their respective preparations.
Pep Guardiola's side have played 13 games since the Premier League returned in June while Lyon have played just twice since March because of the cancellation of the French league.
"Teams such as PSG and Lyon have not really played much football so hopefully we can use that to our advantage but they have got good players," Walker said.
"We have watched a few clips of them and they look a really good team so it is going to be very difficult but we are just going to use the game plan, listen to the tactics from the boss and hopefully that will see us over the line."
Lyon, who finished seventh in Ligue 1, beat City in the Champions League group stages last season and caused a shock by dumping on Italian champions Juventus in the last round.
"I think it speaks volumes in itself," Walker said. "This year they don't have the players that they had when we played against them but, again, they have just knocked Juventus out and you need to be a very good team, very disciplined to beat Juventus over two legs.
"So it is going to be a difficult game but I feel it can swing in our way that it is over just the one leg and we can really attack the game and play every game like a final."