The Reds ran out 2-1 winners at Anfield at the weekend, thanks to a comical last gasp own goal from Spurs defender Toby Alderweireld.
The Belgian inadvertently knocked the ball into his own net after Hugo Lloris inexplicably failed to hold a tame Mohamed Salah header at the back post.
The result ensured that Liverpool returned to the Premier League summit, albeit having played a game more than reigning champions Manchester City.
The title race looks set for several more twists and turns before May and Klopp has revealed he was delighted to scrape over the line against Tottenham to remain in the hunt.
"For me, when we scored [to make it] 2-1, it was a relief as well. It was not like bouncing around and stuff like that," Klopp told Liverpool's official website.
"I have to say, I thought the crowd was unbelievable, really unbelievable. They were not nervous, that's good.
"Nobody was really nervous - they knew it could happen, 'Come on, let's try'. They were really behind us and I love that."
The Reds are chasing their first league crown for 29 years, but they relinquished a healthy seven-point lead over City in the opening two months of 2019.
A frustrating run of draws saw City chase down that gap, but Liverpool have steadied the ship with two vital wins either side of the international break.
Southampton will surely provide another tough test for Klopp's side, but the 51-year-old is certain his players are prepared for the fight ahead.
"We need time together, we need time to train, prepare and all that stuff - and we have that now," Klopp added.
"We don't need a lot of time, but we need it together. We have that now and now let's go again, recover and then fly probably to Southampton.
"It's another team in a really good moment. We will fight again. That's all that I can promise."