With rivals Young Boys beating Anzhi, that strike was the difference between Liverpool going through to the last 32 and getting knocked out.
And after a difficult few months on the fringes of the team, Henderson believes only his third goal in 65 appearances since his £16million move from Sunderland is just the tonic he needed.
"It is always nice to get goals and it was a good moment for me to score," he said.
"I have missed a few good chances in games so it was nice to put one away and hopefully I can keep scoring from now on. I have always tried to improve my goalscoring.
"I think if you score goals then it does give you more confidence.
"You have to keep working hard, keep doing the things you have been doing and it will pay off in the end.
"It is always nice, no matter what type of goal or when it is, to score goals personally and for the team.
"I think everyone is delighted with the performance and the result and for me, personally, I am delighted with the goal."
Progression to the last 32 could have been snatched away with the final kick of the game, however, as veteran forward Daniele di Natale fired over the crossbar.
That would have been harsh on a Liverpool side who, despite manager Brendan Rodgers' (pictured left) decision to field weakened teams throughout the competition, have grown over the months.
It could hardly be called a classic European away display as Udinese, who had Giovanni Pasquale sent off for a second bookable offence with 11 minutes to go, had too many chances, but it was enough to guarantee involvement after Christmas.
"I think overall we are pleased with the performance," added Henderson.
"We went into the game knowing we had to win to go through and that is what we managed to do and everyone is pleased with the outcome."
Liverpool's pre-match preparations for tomorrow's clash with West Ham were disrupted when they were forced to stay overnight in Italy.
The team had been scheduled to fly back to Liverpool on Thursday night, but a problem with their plane meant they were unable to take off and they had to spend the night in a hotel.
Coaching staff tried as best they could to keep to the post-match routine, and it is understood the players undertook a pool recovery session yesterday morning ahead of their return flight.
Meanwhile, injured forward Fabio Borini has revealed he is on the comeback trail.
The Italian suffered a foot fracture in October which required surgery.
But the 21-year-old is confident his recuperation is progressing well and he will be available to play his part in the side's ongoing European adventure from February.
"I'm quite good now -- working hard every day," Borini said.
"The foot is very good and on Monday I see the surgeon to sort out the screws and see if they are taken out or not.
"I'll start working on my ankle and foot, which is better, and my calf is a lot better. The foot always responds very well so that's confident."