Rodgers was full of praise for his £20 million recruit following Sunday's goal-scoring performance against Borussia Dortmund, saying "he is exactly what I've been looking for since Jamie Carragher left".
While his manager's comments were pleasing, the 25-year-old Croatia international insisted he has plenty of work to do as he attempts to live up to the Carragher comparison.
"The manager said he sees me like a leader. I said to him I'm still young. I'm 25, but I will try my best. I will lead the team," Lovren told The Guardian.
"I don't have so much experience like Jamie Carragher but it will come and it is a great honour to be compared by the manager with a player like that.
"I like to talk during the game, I like communication with the lads – to keep me awake apart from anything else. But it's the beginning."
Lovren's arrival at Anfield was on the back of Liverpool's runner-up finish behind champions Manchester City in the Premier League.
Liverpool ended the campaign just two points adrift of City and Lovren is expecting another close contest in 2014-15.
"I can't say that we can win it but we have a really good chance. Chelsea, Arsenal, Manchester United, also Manchester City. They are the ones," he said.
"It will be tight, like last season, but we will be here fighting. I think it will be even better than the last year."
Liverpool kick off their Premier League season at home to Southampton on Sunday.
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