The on-loan Valencia defender was injured in his first Anfield game and his ability on the ball has been criticised in some quarters, but wants to succeed for Brendan Rodgers
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And while he admits he rarely pleases everybody, he is focused on proving his worth until the end of the season when a decision will be made regarding a possible permanent switch from Valencia.
"I usually fail to win unanimous support," he told L'Equipe. "I let people make their own opinion and I give everything on the pitch.
"My goal is to do as much as possible for Liverpool, enjoy every minute, and we'll see what the future holds."
Cissokho made his debut at Villa Park on August 24, but on his Anfield bow just three days later he picked up an ankle injury which forced him off after just 10 minutes and kept him out of action for six weeks.
It was a mixed night for the 26-year-old, who admits he was full of emotions after hearing Kop anthem 'You'll Never Walk Alone' before kick-off that night against Notts County.
"The song had made its mark on me when I was a kid," he added. "It was beautiful, extraordinary. The first time I heard it with the red jersey on my back I felt a lot of emotions. I thought about the path I had taken, all those years working hard to achieve my dream.
"After five minutes, from a tackle, my ankle turned. It was a big sprain. The most significant injury of my career, at the worst time. A piece of cartilage had moved and I had to have surgery in London. It was a very difficult time. I was scared. The operation delayed my adaptation."