The match represented Phillips' first start this season, with the Englishman relegated to the fringes after the return of Virgil van Dijk and Joel Matip from injury and the summer signing of Ibrahima Konate.
However, he will not be involved in the weekend Premier League meeting with Aston Villa thanks to the nasty injury sustained in Italy.
A statement from Liverpool confirmed Phillips suffered a cheekbone fracture during the game, though it is unclear at which point the injury was sustained.
The 24-year-old played on through the break, which will not require surgery, and he is due to take part in a "bespoke training plan" until he is ready to return.
He is likely to be out until the new year, though, with Klopp telling the press Phillips "has to be careful" ahead of an anticipated four or five weeks on the sidelines.
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