Lovren, 29, has largely failed to set Anfield alight since moving from Southampton in 2014, often coming under fire for a lack of consistency at the back, though last season the Croat defender was instrumental in Liverpool's journey to the Champions League final.
Lovren says he remembers his mum took him and they went to the basement and can't remember how long they sat there.
"Modric is the best middle three player in the world and if we win this World Cup, he deserves the Ballon d'Or", he said.
Lovren, who has featured in all six of Croatia's fixtures at this summer's tournament, added: "This is something we will never forget".
"I cannot imagine what will happen if Croatia were to win the World Cup, I really can't".
"It's something special for me", Lovren told beIN Sports."From my point of view, people were saying I had a hard season but I don't agree with that. We showed our character, we showed that we deserved to be in the final and people should respect us", he said. Like with my case, I think people should respect me also.
"But we enjoy to play against big teams, as we showed against Argentina, and have nothing to lose".
"This is something we'll never forget". We will never forget this.
"It was quite tough first half, we couldn't control the ball and they had some chances, but in the second half we did much better".
Croatia played extra-time for the third successive knockout match, having previously beaten Denmark and hosts Russian Federation on penalties.
If Lovren and his team-mates can control Mbappe and manage the alternative threats of Olivier Giroud and Antoine Griezmann on Sunday in Moscow, Croatia will have a genuine chance of pulling off a victory.