The 18-year-old Scottish defender made his Reds debut as a second-half substitute.
Wilson told liverpoolfc.tv: "It was great. It was my first game and there were some nerves before it. But I felt comfortable when I came on, I have been playing with the boys for over a week now and I'm starting to feel part of it.
"It was nice to be involved so early on I wasn't really expecting it. To get my first 45 minutes under my belt is something I can build on in the coming weeks.
"But I think it's a bit too early for me to be thinking of getting into the first team on Thursday for the Europa League game (against FK Rabotnicki)."
He added: "I don't have that high an expectation for this season, I'm just trying to prove myself.
"I am trying not to set too many targets for myself. I just want to settle in as soon as possible and give the manager something to think about, but it'll be up to him how many games I get.
"My aim for the season is to be there or thereabouts."