The goalkeeper was substituted in the second half at Hill Dickinson Stadium following a heavy collision in the build-up to Everton's equaliser.
The incident left him with what head coach Arne Slot described as a "big wound", prompting immediate medical attention and a trip to hospital.
Speaking after the match, Slot confirmed the seriousness of the injury, saying the decision to take Mamardashvili off was necessary to protect the player. Freddie Woodman replaced him between the posts for the remainder of the contest.
Despite the concern, Mamardashvili delivered a positive update the following day. "Thank God everything is fine," he said. "Thank you all so much for your support and for being by my side. I'll be back soon. Big win in the derby and three points."
His message will come as a major boost to Liverpool, who relied on their resilience to see out a tense derby win. The result kept momentum high as Slot's side continued to push forward in the Premier League campaign.
Attention now turns to the next fixture, with Liverpool set to host Crystal Palace FC at Anfield on Saturday, 25 April. Mamardashvili's availability remains uncertain, but his quick recovery message has raised hopes he will not face a lengthy spell on the sidelines.
Nuno Espirito Santo has remained upbeat about West Ham United's survival chances after his side battled to a hard-earned 0-0 draw in the Premier League against Crystal Palace at Selhurst Park on Monday.
Liam Rosenior has backed Moises Caicedo after the midfielder signed a new long-term contract with Chelsea FC, describing him as a player who "leads by example".
Chelsea head coach Liam Rosenior insists he retains the full backing of the club's hierarchy despite a damaging slump that has left their season at a crossroads.
Liverpool are on the verge of securing a major boost at the back, with centre-back Ibrahima Konate closing in on a new long-term contract at Anfield.
