The summer free signing from Chelsea was expected to make a big impact at Anfield but so far it has not materialised.
A pulled hamstring at Bolton on October 31 kept him out for five weeks, with Cole only making his comeback in Thursday night's 1-1 draw against Steaua Bucharest which qualified Liverpool for the last 32 in the Europa League.
During his time on the sidelines boss Roy Hodgson said he felt the England international had confidence issues, saying: "Joe is not a naturally confident character. He suffers when things are not going his way."
However, the 29-year-old dismissed this prognosis.
"No, not at all," was his response when asked whether his confidence had taken a knock.
"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 last night 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."