The Brazil international moved from France to England in May in a deal worth €45 million (£39m/$52m) plus bonuses of up to another €5m (£4m/$6m).
Despite Liverpool's big investment in the 24-year-old, he has been brought along slowly, making just one start and a total of three appearances in all competitions this season.
Though Fabinho has admitted he'd like to be playing more, he insists he is not concerned over his future with the club as he remains patient.
"Of course I want to be playing," Fabinho told Goal. "However, I know I am on a new team in a new league, and it has its period of adaptation.
"I already know the way our coach likes to play, I'm happy here in Liverpool. I hope that I will gradually gain a few minutes on the field.
"The adaptation on the pitch is good, and I’m working and calm, waiting for my moment to arrive."
Fabinho says his mentality has been helped by Liverpool manager Jurgen Klopp and his coaching staff, who have kept him calm while gradually easing him into the Reds set-up.
"From the start he gave me a lot of peace," Fabinho said of the German boss. "He said he knows my quality, the preparation was good.
"We did not have much time in the games, but we're working hard during the week. It's not a problem.
"Not only coach Klopp, but the whole coaching staff has helped me in the adaptation, not only on the field, but also off the field."
Prior to joining the Reds, Fabinho quizzed Roberto Firmino on life in Liverpool, and the attacker helped convince his compatriot to make the move.
"Before signing with Liverpool, I talked to Roberto Firmino about what the club is like and what the city is like," Fabinho said.
"He spoke well of the club and the city, and other people who have already visited the city. The information only gave me more motivation to come to Liverpool."
The Brazilian says his adaptation to life in England has also been helped by his two international team-mates on the club's roster, Alisson and Firmino.
"It's good to have someone who speaks your language in everyday life, especially for me, who does not speak English so well," Fabinho said.
"It is good to have someone who can help with day-to-day life, for me and for my family. This is very important. We are always together, talking or making dinner in someone's home."
Fabinho is currently away on international duty with Brazil ahead of Tuesday's meeting with South American rivals Argentina, and will be hoping to impress ahead of Liverpool's next Premier League outing against Huddersfield Town on October 20.