The Reds will take a two-goal advantage into the return fixture next month after second-half goals from Mohamed Salah and Sadio Mane in Budapest.
Henderson took great satisfaction in every aspect of the performance at Puskas Arena, though warned more work is required to secure a spot in the quarter-finals.
Read on for the captain's post-match interview with BT Sport...
On securing the victory...
It was an important game for us, a tough game. But we're really happy with the performance overall and obviously to score the goals as well and to keep a clean sheet was important for us. Overall, a good night and a good performance.
On the performance...
From start to finish, I thought defensively, throughout the team we pressed really well, won the ball back and looked dangerous going forward. Like I say, a pleasing performance but it's only half the job done. There's another leg to go and it'll be another tough game for us.
On controlling the first half...
I think it was good to be able to create the chances. Yes, we'd have liked to have finished them but I thought the lads reacted well, kept going, kept probing and finally got our reward with the goals. So, really happy overall. I think we've got to be pleased with that because Leipzig are a very good side. But like I said, it's only half of the job done.
On Salah and Mane pouncing on errors to score...
They looked lively all game. I thought they pressed really well from the front and then won it back twice with the pressing and got the rewards with the goals in the end.
On the mentality of the side and returning to winning ways...
Listen, we just want to keep going, keep fighting every time we play. There's a lot of difficult situations throughout the season but I think we've just got to keep going every single game, take one step at a time. Tonight was a good step in the right direction for us and we need to continue that with our form and performance level. If we continue that then we'll get some good results along the way.
On looking ahead to Saturday's Merseyside derby...
It's only one good result. Yes, we're pleased with it and it's only half the job done because there's another leg. But now we've got to turn our attention to the Premier League and the Merseyside derby coming up, which is important. Recover well and we'll give it everything in that game as well.