The former Chelsea midfielder has struggled for form and fitness since his summer arrival.
But Cole told liverpoolfc.tv: "I am happy with everything at Liverpool, I just have to stay fit and keep playing well. No footballer likes being injured, it is a pain, but you have to keep going and keep working hard.
"I got through 75 minutes having only trained once so I'm happy with the way things have gone. It was nice to come back and be out there.
"I just need to kick on and keep myself fit, that is the main thing. If I can do that and get games I'll be very happy as I'll be able to stay on the pitch and help the team to win something."