The Brazilian believes the sky is the limit for the big-spending Russian side, but stressed he will not put himself under pressure to live up to his €35 million [£30.2m] price tag
The Brazilian joined Guus Hiddink's side for €35 million [£30.2m] in the January transfer window after attracting the attention of a host of top European clubs following his displays for Shakhtar Donetsk.
Willian has revealed he made the move with the intention of winning titles, and believes the ambition shown by the club is proof of the heights which they can reach in the coming seasons.
"We’re going to try and win the lot: the league, the cup and the Europa League," he told Fifa.com.
"We’re going to play with ambition. They’re tough tournaments, but when you look at what the club are doing in buying players and putting a strong unit together, then the titles are bound to come.
"The club have got a big future. They’re signing players, putting together a great squad and competing with the richest clubs in Europe, while also fighting it out for the league championship. We've got a strong and well-drilled squad.
"I’ve come here to do the same that I did at Shakhtar: to play well, win titles and take the club as high as they can go. In short, my aim is to win."
Willian accepts there is a certain level of expectation at the club due to his hefty price tag, but insists he does not feel under pressure in his new surroundings.
"Obviously they’re going to want a return on that, but I've got to stay cool,” he added.
"I can’t put pressure on myself when I go out there. I've got to let things happen naturally so that I can show they made the right decision in spending that money."