The £16million summer 2011 signing from Sunderland was part of a big-money squad overhaul conducted under former boss Kenny Dalglish.
But Henderson only made his first Premier League start of this season under new manager Brendan Rodgers in the weekend draw at Swansea City after being restricted to substitute, Capital One Cup and Europa League appearances.
The 22-year-old has been offered encouragement from Rodgers but knows he still has to prove his credentials at five-time European champions Liverpool.
Henderson said in the Daily Star ahead of Wednesday's game at Tottenham Hotspur: "If you move to a club like Liverpool, you have to try to make it for life and not just for Christmas.
"When I signed for Liverpool, I definitely wanted it to be long-term and I will give it everything I have got.
"It is a lot easier to throw a tantrum and walk away from a big club than fight to make it work, isn't it?
"Other players might treat it different ways but it just gives me a different incentive to push on and go forward.
"I think the manager has seen that I have improved since he came to the club and I need to keep on improving."