But there were more pressing concerns for Jürgen Klopp after it emerged that Grujic was sent to the nearby Huntingdon Memorial Hospital at half-time after being forced off by a clash of heads with Bertrand Traore.
The Serbian midfielder, who Klopp revealed in his post-match press conference had no recollection of the incident, was given an all-clear after undergoing a CT scan.
However, the 20-year-old will not be allowed to play against Milan as Liverpool's medical staff continue to monitor his progress and ensure a full recovery.
No period has been given as to how long Grujic could be sidelined, but concussion injuries can take up to two weeks to recover from.
That could leave him in doubt for the Reds' other pre-season games, against AS Roma in St. Louis on Tuesday, and clashes with Barcelona and Mainz next weekend.
Reds' midfielder to miss clash with Milan as precaution
There were fears that Ragnar Klavan had also suffered an injury after being the victim of the late lunge that saw Chelsea midfielder Cesc Fabregas awarded a straight red card.
But Klopp confirmed afterwards that the debutant defender had escaped unscathed, as well as revealing that Fabregas went into their changing rooms to apologise for the poorly-timed tackle.
Although Grujic won't play any part in Santa Clara against Milan, the Reds could hand a debut to Georginio Wijnaldum - who missed out on the squad against Chelsea to remain at the club's training base in Palo Alto to continue fitness work.
Daniel Sturridge, Nathaniel Clyne, Christian Benteke, Divock Origi and Simon Mignolet were among the others not involved, while Emre Can returned to the camp earlier this week but could find it too soon to feature against the Serie A side.
Sturridge enjoyed an extended summer break to ensure he was refreshed and ready, instead staying at Stanford University to undergo extra fitness sessions rather than facing his former club at the Rose Bowl in Pasadena.
But he should be drafted in for their second game of the tour, also in California, while Clyne could return from a tight hamstring problem.
Belgian trio Benteke, Origi and Mignolet were not involved having only returned from international duty a few days before the game.
They are all likely to be put on extra intense programmes to ensure that they reach the same levels of fitness of the rest of Klopp's first-team squad by the start of the season, just over two weeks away.