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The Reds remain in third, nine points clear of fifth-placed Arsenal, who have three games in hand.
"Today you could feel it immediately in the dressing room," he said.
"Everybody was like, 'that's very important'. Of course, we have to keep on proving it, but it feels outstandingly good in this moment."
He added: "This was massive, it's absolutely massive.
"That's how it feels. We have won a few games this year, but this was really special."
The Reds fell a goal behind just before half-time when Jon Walters headed in Xherdan Shaqiri's cross.
But two second-half goals from Brazilian substitutes Roberto Firmino and Philippe Coutinho saw Liverpool seal an 18th league win of the season.
The pair had started on the bench, with Klopp saying Firmino had been suffering from exhaustion after his recent exertions for Brazil, and Coutinho had lost three kilograms (6.6 lbs) in the past week due to illness.
"At half-time it was a difficult decision to make because it was not clear that Roberto and Phil would be ready for 45 minutes," Klopp added, whose side have 12 more points than they did at this stage last season.
The Reds' next league game is at West Brom. They do not face any teams in the top six during their final six matches of the season.
Former Manchester United and Everton defender Phil Neville
"Having seen Liverpool's starting XI, I fancied Stoke to win this because their opponents were missing their front four of Coutinho, Firmino, Sadio Mane and Adam Lallana.
"They were all over the place in the first half. The Stoke goal was a poor one to give away.
"The game changed after Klopp brought the Brazilian pair on. Liverpool started to dominate possession.
"This was the most important three points of the season for the Reds."
Manager Jurgen Klopp hailed Liverpool's 2-1 win over Stoke as "massive" as his side strengthened their grip on a Champions League spot.