Grujic joined the Reds from Red Star Belgrade for £5.1million in January, before officially moving to Anfield in the summer.
Despite an impressive pre-season in which he scored three goals, including a superb header against Barcelona, the 20-year-old has made just one appearance in 2016/17 to date.
Grujic is not expecting too much from his first year at the club, but says he will learn from his teammates ahead of what he hopes will be a strong second season.
“It was hard in pre-season, especially for me because I have come from Serbia and our work here is at a higher level,” he told Liverpool FC Magazine.
“The running and exercises are harder and I’m still learning, but I’m sure I will adapt. I’m proud that I can work with the staff here and it will be OK.
“For the first season I just want to learn from these guys. I have the big pleasure of playing with some of the best footballers in the world. I want to get some minutes and games to try and improve myself for the future.
“I think next season will be the one where I show what I can do.”
Grujic also discussed the sheer enormity of representing Liverpool, and believes there are parallels to be made with Red Star, in terms of the relationship with the fans.
“I think there is the same harmony between club and fans and already everywhere that I’ve been around the city I just feel how Liverpool is such a big club.
“All around the world people support Liverpool, that really struck me on the summer tour, and there is incredible harmony between fans and players.”
He will still likely be given a chance to shine in cup competitions, though, as he adjusts to the fast pace of English football.
At 20, the Serb is still a very young player, and no unnecessary pressure should be put on him at this stage in his career. His potential is huge, and in the long-term, he can become a key man for the Reds.