The Switzerland midfielder helped Bayer win a first ever Bundesliga title in his first season with the club.
He said, "We want even more. Not only this year, but obviously we want to play at the top in the coming years.
"We know that the pressure is a little higher now than last year. This also depends on us. But of course we want to be able to handle the pressure well. That's why it is necessary for us, the more experienced players, to put ourselves alongside young people. And we must not think that everything will resolve itself."
On leaving Arsenal, Xhaka said: "For me it wasn't a step back, but rather two steps forward. Because I had the precise feeling, discussing with the coach (Xabi Alonso) and with (sporting director) Simon Rolfes, that something special could happen here in the next few years."