Fikayo Tomori had given Milan, who needed to win and a favourable result between Porto and Atletico Madrid, hope they could make the last 16 with his tap-in just before the half-hour mark at the San Siro.
But a quick reply from Mohamed Salah and Divock Origi's nodded finish 10 minutes after the break ensured Jurgen Klopp's side, missing a raft of starters, finished Group B on 18 points, the first English team to achieve that total.
"It's an exceptional performance... with that many changes, the boys have to be confident enough to show how good they are," Klopp told reporters.
"I saw so many good things tonight it was unbelievable."
Serie A leaders Milan, who were missing half their starting back four and other first-team players including forwards Rafael Leao and Ante Rebic, were condemned to last place thanks to Atleti's 3-1 win at Porto which put the LaLiga side through in second behind Liverpool.
Defeat for Milan ensured they failed in their attempt to make the Champions League knockouts for the first time since 2013 and leaves them without even Europa League football in the new year.
"We need to put this anger and frustration aside as we know we have developed as a team," said Milan's Alessandro Florenzi.
"If you look at our defeats they were not heavy losses, they were all one goal defeats... Tonight we were on an equal footing with a great team.
"We are a level below Europe's best sides but it's a gap that we can close."
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