Lovren was abused and widely criticised on social media for his poor performance in a match in the 4-1 defeat by Tottenham last month.
The Croatian admitted he received death threats against his family on Instagram that read: "I'm gonna murder your family."
"I would just love to finally get that 'black cloud' away from me, so things can get better," the Daily Star quoted Lovren, as saying.
"You simply cannot change what has happened in the past," the 28-year-old said.
Lovren added, "It's not easy for me. Maybe it's interesting for everyone else, but I guess it'll be better soon."
Lovren will play for Croatia against Greece in World Cup play-offs this week. (ANI)