Liverpool also meet fourth tier Exeter City in the third round of the FA Cup next month.
"We're all focused on fighting for trophies and I think we have a great chance in the competitions we're in," Coutinho told the club's website (www.liverpoolfc.com).
"Three wonderful years. In the beginning I was given a very warm welcome from the fans, the team, everyone who works here.
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"I'm very grateful to the club and now I hope to be able to help the team win trophies, it's very important to keep battling," added the 23-year-old.
Coutinho joined Liverpool, who are without a major trophy since they lifted the League Cup in 2012, from Inter Milan in January 2013 for a fee of 8.5 million pounds.
He has scored four goals in nine games since Juergen Klopp took over as manager in October and, being a focal point of their attacking moves, Coutinho said his desire to improve remained strong.
"We learn little by little," said the Brazilian. "When you arrive here the football is very different, the style of play, it's more intense, you use your body more, it's faster.
"These things I think I've improved on since I arrived, as I came from a different style of football, and I hope I can continue to improve."
Liverpool host shock leaders Leicester City in the Premier League on Saturday.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by Tony Jimenez)
