Grujic was manager Juergen Klopp's first signing when he joined the Merseyside club from Red Star Belgrade in January and the 20-year-old made his first appearance for Liverpool in their 2-0 Premier League defeat by Burnley last month.
"It was hard in pre-season, especially for me because I have come from Serbia and our work here is at a higher level," Grujic told British media.
"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."
Grujic scored five goals in 21 league appearances for Red Star last season and was also a member of Serbia's under-20 squad that won the World Cup in 2015.
"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."
Liverpool, who are sixth in the league standings, travel Chelsea at Stamford Bridge on Friday.
(Reporting by Ian Rodricks in Bengaluru; editing by Amlan Chakraborty)
