The England international moved to Anfield in the summer after making a £20m switch from hometown club Sunderland.
"I think I have settled in okay. I am enjoying my time here and the lads have been brilliant, as well as the fans," Henderson told Sky Sports News.
The 21-year-old appreciates that the competition for places is fierce and is now keen to improve and secure himself a regular starting berth.
"I now need to kick on and do even better," he added
"Given the opportunity, I need to take it and make sure I stay in the team."
Liverpool host rivals and Premier League leaders Manchester United at Anfield on Saturday.