The former Chelsea star has struggled since his summer arrival on Merseyside.
Cole told Liverpool's official website: "It's not gone how I would have liked, but that's life. Things like that happen and you've just got to push on through the difficult times.
"I've had plenty of good times in my career and I've had my share of difficult times, and I'll always come through.
"I'm determined to be a success here. I'm working hard every day. The main thing is the club - it's all about Liverpool.
"I'm pleased it (the team's form) has turned around and we're going in the right direction, and if Liverpool can keep going there, I'd love to be part of it."