The Reds went into the match knowing that defeat would likely see them crash out of the competition just over six months after lifting the trophy, but their win ensured that they topped the group ahead of Napoli.
Liverpool will subsequently go into pot one for Monday's Champions League draw alongside the likes of Barcelona, Bayern Munich, Juventus, Manchester City, RB Leipzig, Paris Saint-Germain and Valencia.
Jurgen Klopp's side will not be paired with any of their fellow group winners, and will also avoid compatriots Chelsea and Tottenham Hotspur in the next round.
With Napoli out of contention too, the defending champions have five potential opponents in the last 16: Atalanta BC, Atletico Madrid, Borussia Dortmund, Lyon and Real Madrid.
The latter would be a repeat of the 2018 final which Liverpool lost, while there could also be a return to Dortmund for Klopp, who led the German club to the 2013 Champions League final.
The Reds have never beaten Lyon, while they have only won one of four meetings with Atletico and have never faced Atalanta before.
The Premier League leaders will learn their fate when the draw takes place at 11am in Nyon on Monday, with the first legs due to take place on February 18 and 19.