The Reds stay second in the Premier League, level on points with current leaders Tottenham Hotspur, after a 1-1 result at Craven Cottage.
And Jürgen Klopp's men welcome Spurs to Anfield in midweek, providing the opportunity to return to winning ways and go top.
Speaking to Liverpoolfc.com following the Fulham draw, Henderson said: "Another big game comes quick around the corner.
"A big game for us and we need to recover well, get ready and prepare for that one.
"The Premier League is competitive and no matter what position you are in on any given day, it is always a tough game. We knew Fulham would make it difficult and they did that.
"We've just got to keep going. There's a lot of games over a short space of time but it's the same for everyone – demanding, injuries and stuff like that, but that makes us stronger as a squad.
"And the players that come out and play on a matchday will come out and give everything for the three points in the end. I think the lads did that."
A slow start from the visitors in London on Sunday was punished as Bobby De Cordova-Reid's well-taken finish gave Fulham the lead after 25 minutes of play.
But the opening goal did draw a positive response from the Reds towards the end of the first half and they levelled in the 79th minute through a Mohamed Salah penalty.
"It wasn't like us. It was all over [the field] really," Henderson said of the game's early phase. "I felt we were a little bit late to second balls, we weren't winning headers and when you lose them individual battles it's difficult.
"I don't know what the reasoning behind that is but we've got to take that and make sure that doesn't happen again going forward, learn from it and keep doing what we did after that.
"I thought there was some really good stuff and we dominated the game for large parts, created one or two, not loads of chances, but one or two – enough to win the game.
"So, there were still good things but still things for us to improve on."
On what Klopp said to the players at half-time, the captain revealed: "Start the second half like we finished the first and keep going, keep the momentum going.
"In the last 15 minutes of the first half, we had that momentum, winning the ball back higher up and creating one or two half-chances. So to continue that and hopefully get back into the game and find a way to win.
"Unfortunately, that wasn't the case but we managed to come away with a point. We've got to take that, we've got to learn, improve and move on."
Joel Matip was taken off at the break after suffering from a back spasm. His withdrawal required Henderson to drop deeper and operate as a centre-half for the remainder of the contest.
Asked whether that transition was made easier because Liverpool were spending more time in Fulham's half, Henderson replied: "We had a lot of the ball, which helps, so, yes, that did help a little bit.
"But there were still times where I had to defend – set-pieces or counter-attacks and things like that. So I've got to make sure that I'm switched on all the time, especially playing in a new position.
"But overall, we could have come away with the three points in the end but we got punished for our start to the game. That was unlike us, so hopefully it doesn't happen again."