The Reds were four goals up after 42 minutes of play on Friday night as Anfield welcomed the return of the European champions.
"It was the start of the Premier League, we wanted to go out and start really well, which we managed to do," the captain told Liverpoolfc.com.
"We scored some brilliant goals and played well in the first half. In the second half we created some chances, but could have controlled the game a little bit better.
"There's still improvement [to be made] but overall we're delighted with the result and performance.
"It wasn't so much defensively, we gave the ball away sloppy at times and we didn't control the game with the ball, so in the transition we weren't in great positions. That's one thing we can improve on.
"But it's the first game of the season – there's going to be things that we need to improve on, look back on and work on. That's only a positive for us.
"We'll learn from tonight and want to improve in the next one."