The 23-year-old moved to Anfield for £18million on transfer deadline day, with Reds managing director Ian Ayre describing the France international as the club's "marquee signing" of the summer.
Sakho had dropped down PSG's pecking order following the arrivals of Brazilian duo Thiago Silva and Marquinhos, who joined their countryman Alex at the Parc des Princes.
He also found himself surplus to requirements for his country.
But his move to Merseyside has revived his career, leading to a call-up from Les Bleus for their World Cup qualifier against Finland at the Stade de France and a friendly with Australia in Paris.
"I had to quit Paris to get back in the France squad," he said in an interview published in Le Parisien newspaper on Tuesday.
"Being picked again proves many things. That I still have that level. Most of all that I didn't leave to join a big club because of the competition (at PSG).
"At Liverpool there are also very good players in my position, but the competition is clean. At Paris it had become complicated.
"I don't want to break sugar on anyone's back. I could say many things about certain directors at Paris but there's no point.
"I've put that behind me and closed the door. The day I decided to leave PSG, I just got on with it."
Sakho has flourished playing in a back three for Liverpool in recent games, lining up alongside Martin Skrtel and Kolo Toure during 3-1 wins over Sunderland and Crystal Palace.
And he has credited Reds boss Brendan Rodgers for helping him to settle both on and off the pitch.
He said: "I'm taking English lessons. As for the football, it's not lived in the same way.
"I'm learning and I listen to the manager's advice. It's funny, he calls me Killer.
"On the pitch I'm trying to adapt to my team-mates. And things are getting better and better because I need to communicate."
Sakho shed a tear when being interviewed ahead of PSG's clash with Monaco last month, just three weeks after leaving the club following an 11-year stay, but insists he has no hard feelings over his departure.
"Some people said I shouldn't have done that (cried) with respect to Liverpool," he said. "To them I apologise for having spent half my life in Paris, for having had teachers who helped me to grow up as a man.
"More seriously, though, it's obvious that I have a strong connection with PSG and that I didn't leave without emotion.
"The moment of the interview I was thinking about my father Souleymane who passed away when I was 13.
"My mother was in the stands and I told myself that I'd have also liked to see my father watching me in that moment. I know he would have been proud of his son, and that's when the tears flowed."
Sakho admits PSG will always remain close to his heart, adding: "I remain a Paris fan for life. I saw the match against Marseille (a 2-1 win with 10 men on Sunday) in a restaurant. With every goal I got up to sing: 'Here, it's Paris'."