The France international found himself down the pecking order at the Parc des Princes after the arrival of Brazilian trio Alex, Thaigo Silva and Marquinhos in recent seasons, and opted for a move to Anfield on deadline day, signing a four-year deal.
Sakho made 196 appearances for PSG in seven seasons, but is now focused on winning his place in Brendan Rodgers first-team plans - which he believes will be a tricky task.
"I achieved beautiful things at Paris that I am very proud of, so I can leave raising my head high," Sakho told L'Equipe.
"Since the start of my career, my first desire has been to go on improving and reach the objectives I set.
"My career dictated me that choice. I take on without regret. I am joining a great club with fantastic fans. I am very proud to have signed at Liverpool.
"Early in the summer I had talks with my PSG coach and chairman. Some things were said but not necessarily with any result. But there is no problem and I feel not bitterness. It was my choice to leave. No one pushed me to the exit door.
"Contrary to what I could hear, I don't fear competition. At Liverpool, do you believe there will be no competition in my position?"
The 23-year-old revealed that the atmosphere generated at Anfield as he watched his new team beat Manchester United on Sunday was crucial in making his mind up.
"Why Liverpool? Because Premier League is the best league in the world, and it was the club that proposed me the project that suited me the best," he added.
"The officials knew how to convince me.
"My first feelings in the Anfield stands confirmed to me that I made the right choice. They are amazing fans and a very good team. The fans' chants are beautiful even if I can't understand English so far!"
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