The Reds are winless in their last four Premier League outings, while they have failed to score in their previous three as they continue to struggle with creating chances.
Despite playing Manchester United off the park in the opening 30 minutes at Anfield, Liverpool were unable to make their superiority count as they failed to get any of their eight attempted shots on target.
United edged back into the game as the clock ticked on and ended the 90 minutes with the slight upper-hand. Alisson was forced into two excellent saves as he kept the Reds within touching distance of the league leaders.
Henderson, who partnered Fabinho at the back amidst Joel Matip's continued absence, spoke to LFCTV after the game as he insisted it's the squad's collective responsibility to ensure the Reds start notching again.
Read on for everything the Reds skipper had to say...
On whether both sides would be satisfied with the result...
"Not really. I think being at home and the performance level from us was very good so a little bit disappointing we haven't got the win. I think the quality that we've got, we should take one of the chances at least.
"But it can happen in football sometimes, we just aren't getting the rub of the green inside the box at the moment. We've just got to keep going and working hard and I'm sure that little bit of luck will change."
On Liverpool's lack of goals in recent games...
"We need to score goals to win games. I'm not just talking about the front three, by the way, I'm talking about everyone. Midfielders and full-backs getting into the box, set-pieces. Everybody can chip in so we need to start doing that.
"Like I said, that little bit of luck hitting or ricocheting someone and going in, because we had good enough chances to win the game. I think we can be pleased with the performance level.
"We gave everything to try and win the game but unfortunately, we just couldn't that goal - which we find ourselves keep saying over the last few weeks so that needs to change quickly."
On how the Reds defended...
"Fabinho's been outstanding there for the majority of the season. I thought we defended quite well as a team. United are dangerous on the counter and dangerous in the final third with the players they've got.
"They had one or two chances but I thought we limited that today and defended pretty well for the majority of the game, so I think we can be pleased in that sense.
On Alisson's contributions during the game...
"He makes big saves. He has done for a long time and that's what we need him for. He stepped up to the plate again and kept us that clean sheet."
On where Liverpool need to improve in the upcoming weeks...
"I think the performance today was very good. We kept going, worked hard right till the end and kept pushing. Again, it can happen sometimes in football where you can't quite find that goal or last pass in the final third.
"We're all human. You can see when we miss chances, we're a little bit down confidence-wise. But we need to keep going to try and find that goal. We've just got to keep working hard and not think about it too much.
"The quality we possess going forwards is frightening so it's not the quality. We just need to change our mentality a little bit and make sure we're ruthless when we're in front of goal. That's not just the front three, that's everybody that gets into the box and gets the opportunity to score.
"That's something we haven't said for a long time as we've scored a lot of goals. But that's one thing we need to change quickly because today, defending-wise, everybody throughout the team defended very well.
"I thought some of the football was outstanding, we played some great stuff. It's just that last little bit. There's still plenty of games to go and we need to keep pushing right till the very end."