The 18-year-old had to make way after just 28 minutes and was replaced on the field by veteran Jay Spearing.
"Unfortunately, that's not a good one," he said. "He teared [sic] his lateral meniscus, which needs surgery. That one will take a longer time."
Typically, an injury of this type can take anywhere between three and six months for a full recovery.
But despite the setback, Lijnders expressed confidence in Doak's resilience: "He is young, he is a fit guy, he is a positive guy, so for sure he will come back stronger."
"We need him to come back with the same fire he has with the ball, how he was," he said, adding: "We will wait for him."
A top talent
Rated as one of the top young talents at the club, Doak has been on the periphery of the first team this season after making his senior Liverpool debut during the 2022/23 season.
The young winger has made five first-team outings in all competitions for Jurgen Klopp's side so far this campaign, with the latest coming during the Reds' 2-1 Europa League defeat away to Union Saint-Gilloise.
Doak also made his Scotland Under-21 debut earlier this year, prompting senior side boss Steve Clarke to hint at the possibility of a call-up ahead of Euro 2024.
He told Football Scotland: "He has talents that maybe we don’t have in the squad. But you have to allow young players to develop and find their own game. Every now and again you get the odd one that comes through."
Better news for Gravenberch
Meanwhile, Tuesday's injury update from Lijnders also shed light on the conditions of other players within the Liverpool squad. More positive updates were provided on Ryan Gravenberch, Alexis Mac Allister and Diogo Jota.
Gravenberch underwent a scan after limping off during Liverpool's goalless draw with Manchester United on Sunday, and it revealed a less severe prognosis than feared. "It’s only DOMS, which is fatigue, so that’s a really good thing," Lijnders explained. "He will train hopefully today. Let’s see where he is."
Lijnders also delivered good news about Argentinian midfielder Alexis Mac Allister and Portuguese forward Diogo Jota.
“Alexis is progressing well; he doesn’t have pain anymore, which is a good thing," he told the press, adding that Jota had now upped his recovery and was now taking part in "ball work on the pitch".