Coutinho's hat-trick was his first for the club and he hailed the achievement of making the latter stages of the Champions League as a significant moment.
"It was a special night due to the result and because I had the armband in such an important game playing for a club like Liverpool," added the player, who captained the side at Anfield.
"For sure this is my most important hat-trick. In the Champions League it was my first one. I scored one for Brazil but this was more important."
Defender Joe Gomez said Europe's top clubs have every reason to fear Liverpool.
They finished the group stage with 23 goals — second-highest in the all-time list behind Paris Saint-Germain's 25 from the current campaign — and although they avoided the likes of PSG and Barcelona, potential last-16 opponents include Bayern Munich, Juventus and Real Madrid.
"We believe we can beat anyone and we have to have that mentality," said Gomez.
"We have great quality and they can be scared of us the same way we can be wary of them so that's good."