Milner was one of just two players retained by Jurgen Klopp from Thursday’s Premier League win over Sheffield United, with Joe Gomez also starting.
But the 34-year-old lasted just nine minutes and was replaced by youngster Yasser Larouci after appearing to pick up a hamstring injury.
Milner will be assessed by Liverpool’s medical department over the coming days in order to learn the full extent of the injury.
“He has pain, that says it’s serious,” Klopp said. “It’s [his] muscle.
“Let’s start with the negative things. Two players started the last game and one got injured. That’s the situation we are in.
“That’s why a lot of managers make changes. It’s nothing to do with the Cup, it’s the timing.”
Liverpool are currently lacking options in midfield, with Fabinho yet to return from an ankle injury and Naby Keita sidelined with a groin problem.
Elsewhere, Dejan Lovren, Joel Matip and Xherdan Shaqiri are all unavailable through injury with a league trip to Tottenham Hotspur in six days.
But Klopp can count on Alex Oxlade-Chamberlain once again, as the 26-year-old returned from an ankle problem to make an appearance off the bench.