Captain Henderson came off the bench to inspire the comeback win on the south coast, assisting Mohamed Salah’s superb 80th-minute effort before tapping home to end the contest six minutes later.
Henderson credited manager Klopp for the team’s desire to battle for the full 90 minutes.
“The manager has been big on that. He was big on that when he first came in a few years ago – that no matter what happens in the game, we still fight right until the very end,” Henderson told Liverpoolfc.com.
“That is what we have been doing for a long time now and we need to keep that mentality going and not stopping until that final whistle goes.
“It was a must-win (game), we knew that, so it’s a big result for us going forward.”
England international Henderson and fellow midfielder James Milner were dropped to the bench by Klopp at St Mary’s following Sunday’s last-gasp win against Spurs.
The pair were introduced as a double substitution 31 minutes from time with the score level at 1-1 after Naby Keita’s first goal in English football cancelled out Shane Long’s early opener.
Asked what his manager said before he came on, Henderson replied: “Make a difference.
“Use our experience and then make a difference. Help the lads, get them going because we were under a bit of pressure.
“We kept going right until the end and we kept fighting and thankfully we managed to score a couple of goals and win the game.”