The France international joined Liverpool in a £15million deal from Paris Saint Germain on transfer deadline day.
"I achieved beautiful things at Paris that I am very proud of, so I can leave raising my head high," Sako 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 move on without regret. Today I am joining a great club with fantastic fans. I am very proud to have signed at Liverpool.
"Early in the summer I had a talk 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?"
"Why did I not leave PSG next January as free agent? I wanted to pay back PSG for what it brought me." added Sakho.
"Of course it would have meant a big financial jackpot for me, but it was not my choice. I wanted the club to take advantage of it too."