Omar Alderete's first-half header earned Sunderland the 1-0 win.
Xhaka said afterwards: "We had a gameplan and we knew that it would be very difficult here but what a mentality from the team. This is exactly what we need.
"What a support from the fans. It looks good to win like this because of course I think Nottingham were the better team today but football is not about who is better on the pitch, it is about who scores more and we won today and we are very happy."
On why he joined Sunderland, Xhaka added: "First of all the project. They brought me here for my experience and leadership and what I can bring to the team and I am trying day by day and week by week to show the guys how professional you have to be at this level. They make my life easier.
"Even at my age now, they run, they fight - the mentality that this team has is unbelievable. There are so many more things to come but first of all I am happy that I am here with this team and this football club."