The Spaniard gifted Ollie Watkins a goal with a sloppy pass out from the back towards Joe Gomez and the Reds failed to recover, suffering a shocking 7-2 defeat.
Grujic, who has joined Porto on loan, believes Adrian may have played his last game for the Reds, who are without No 1 Alisson after a shoulder injury suffered in training.
“The first couple of games the man is nowhere to be found,” Grujic said in a reply to a post on Instagram. "I impatiently decided to move him [out of my team] in Fantasy [League]…. the rest is history.
Grujic then added: "Probably also ended Adrian's career at LFC".
Adrian’s struggles come with Liverpool welcoming Brazil's Under-17 goalkeeper Marcelo Pitaluga from Fluminense.
The Reds were able to edge out competition for the shot-stopper due to Alisson’s brother Muriel, a fellow keeper, playing alongside the talented youngster last season, which helped notify the club to eventually pay around £1.8million to bring him to Anfield.
Jurgen Klopp's side have been tracking his progress after Pitaluga helped Brazil win the Under-17 World Cup as hosts in November last year.
It is the latest incident for Adrian with pressure mounting after a dreadful mistake cost the Reds in their Champions League last 16 defeat to Atletico Madrid last season.
Klopp looked to ease the pressure on Adrian after the defeat to Villa, while also revealing Alisson is likely to miss six weeks.
“The first goal was not good but I don’t think he had anything to do with the other goals,” Klopp said. “We didn’t help him tonight.
“He is a really good goalie. Last year we played 11 games with him and won pretty much all. Tonight our goalie was not the problem. The reaction to the first goal was not his problem, it was our problem.
“It is not often I have seen games like this. I am old enough to know strange things can happen in football. You could see in moments that in challenges Aston Villa wanted it more and that is something I saw and I don’t like.
"We were slightly fortunate but it is not that he can play against Everton," Klopp added. "I don't want to put a time frame on it but it looks like four weeks could be possible.
"I think six weeks is maybe more likely but I don't know. So we have to further assess this thing and that is how it is."