The 20-year-old clashed with Blues winger Bertrand Traore in the first half at the Rose Bowl in Pasadena, and was replaced by Adam Lallana at the interval.
Subsequently taking to hospital to assess the damage caused by Grujic’s head injury, the Serbian revealed he had no memory of the challenge.
Speaking after the Reds defeat, settled by an early Gary Cahill header, Jurgen Klopp expressed his concern over Grujic’s condition, saying pre-season injuries were his “biggest problem.”
“Hopefully it’s not too serious but of course a young boy in this situation is not too cool.
“Injuries after games like this in pre-season is the biggest problem obviously.
“That’s a challenge that can happen and is unlucky, but not too good for us.”
Grujic has impressed throughout pre-season so far, suggesting he could become a key player under Klopp in 2016/17.
While Traore’s challenge was innocuous, merely vying for the ball in the air, the German will be left frustrated by the fierce nature of the contest on the whole.
Klavan escaped injury despite the severity of the tackle, but it remains to be seen whether Grujic will fares any worse.
Given the nature of Grujic’s head injury, the midfielder could miss Sunday morning’s International Champions Cup follow-up against AC Milan, taking place at the Levi’s Stadium in Santa Clara.
This comes as a blow to the Liverpool manager, who will be hoping to field his strongest squad at some point during pre-season.