Signed in the summer from Hungary's Puskas Akademia, the 21 year-old goalkeeper has trained with the senior squad and featured at Anfield with the U21s.
"It was very nice to come here," Pecsi told Liverpoolfc.com. "Everybody helped me a lot. I feel at home now.
"When I first heard it could be possible that I could sign for Liverpool, it was a proud feeling and good feeling that the years I put the work in, I can make a step up in my life and my career, and I can come here and learn from world-class players and experienced coaches.
"It was a really good feeling but this is what I always wanted. This is what I worked for."
On the influence of fellow Hungarians Dominik Szoboszali and Milos Kerkez, Pecsi added: "They helped me a lot, especially Dom because he's here for a longer time. He helped me a lot.
"When I want to ask him something or get help, he always helps me. I think we get along good. It was good that sometimes I could speak to someone Hungarian or if I didn't understand someone or ask about something or how things work here, it was easier to explain in Hungarian and he was here.
"Of course when it comes to football and we speak about football, in this part he can also help me a lot. When I see the guys or him in training, it's a big inspiration in the big level they show every day."