The 26-year-old joined the Reds for £16m from Sunderland in 2011 and has cemented a spot in the first team in recent seasons.
Henderson told reporters: "I feel as though I have matured a lot and I can deal with it in my own way. I can do more things.
"The more pressure, the more I like it. I think that will be the same for quite a lot of the lads as well."
Henderson has made 105 appearances for Liverpool and has featured 15 times for England since arriving at Anfield.