Everton are the only British side left in the Europa League after they beat BSC Young Boys 3-1 to go through to the last 16.
Romelu Lukaku scored two goals to reach a total of five in the tie, which ended 7-2 on aggregate.
Liverpool lost their first European penalty shootout as Besiktas knocked them out on Thursday night.
Tottenham also failed to go any further, losing 2-0 on the night to Fiorentina. Celtic lost 1-0 to Inter.
The Glasgow side battled bravely in Milan after Virgil van Dijk was sent off after 36 minutes, but they couldn't compete with just ten men.
A stunning strike from Fredy Guarin just before the final whistle saw Celtic's European campaign end.
Belgian striker Lukaku added to his hat-trick in Everton's 4-1 first leg win in Switzerland with two more goals after Sekou Sanogo had given the visitors the lead.
Then Kevin Mirallas made it 3-1 before half-time to make things easy for Everton. They'll find out who they face in the last 16 on Friday.
Liverpool's first ever penalty shoot-out loss in Europe came as Tolgay Arslan scored for Besiktas.
With the tie 1-1 at full-time, it was time for penalties. Liverpool defender Dejan Lovren missed the deciding spot kick, leaving the score 5-4.
Tottenham boss Mauricio Pochettino says his side must recover quickly after their 2-0 loss to Fiorentina left the tie 3-1 overall.
Spurs play their London rivals Chelsea in the League Cup final on Sunday.