Klopp's side came from a goal behind to overcome the Potters by two goals to one at the Bet365 Stadium, with second-half substitutes Philippe Coutinho and Roberto Firmino's goals proving sufficient to deny the hosts three points.
Speaking with reporters in a post-match press conference, the former Borussia Dortmund coach expressed his optimism that the way in which the win was achieved - with his side not playing as well as they could - will be a catalyst for a turnaround in form.
"We won a few games this year but this is really special," the German said. "You could feel it immediately in the dressing room. Everybody was like: 'That's very important.'
"Of course we have to prove it next week and the next week - that's how it is. But it feels outstandingly good in this moment," he continued.
"I can imagine Stoke feels the exact opposite because they were really close to getting points today - all three or maybe one. But at the end, we all worked really hard for the three points and we got them," the 49-year old added.
Klopp also singled out the performance of Simon Mignolet. The Belgian goalkeeper made two astonishing saves to keep his side on course for the victory.
"We needed Simon Mignolet with two outstanding saves - the second one was one of the best I've ever seen, Save of the Day, Month, Year.
"It was outstanding, well deserved for him because he has got a lot of criticism in his Liverpool career," he added.
"Sometimes these are the moments you need as a player, and for us as a team we need a goalkeeper in a moment like this."