Ayoze Pérez's wonderful first-half header secured United's first league away win of 2019 as Rafa Benítez's side moved into 13th place on 38 points - ten points clear of the relegation zone.
Dúbravka's previous clean sheet came in Newcastle's 2-0 triumph against Burnley in February and, after waiting five league fixtures to reach double digits, the 30-year-old heavily praised his teammates for the Magpies' important victory over the Foxes to enhance their chances of safety.
He told nufc.co.uk: "It is an amazing feeling to get the win. The lads in front of me played a fantastic game and, although it was a tough match, they all put their bodies on the line, battling hard as well as scoring a very nice goal.
"We knew it would be a difficult game. Every time we play against Leicester, they try to control the game and you could see they were pressing really high and we didn't have much possession but all of the players, not just the back five, defended really well.
"Every ball that came into the box was being cleared and it was difficult to keep the ball due to Leicester's high pressing. However, when we had the ball, we tried to be dangerous in attack and, overall, we scored one more goal than them which is the most important thing.
"It is a special feeling to achieve my tenth clean sheet of the season. I know how long we have waited for it and now we have it as well as being in a much better position. We have another four games ahead of us and I think the pressure is not as high as before."
After recent league defeats against Arsenal and Crystal Palace, Dúbravka was pleased to revert back to winning ways against an in-form Leicester side, sitting in a respectable seventh place after a four-game unbeaten run.
And, backed by over 3,000 Newcastle fans, the shot-stopper revealed his amazement of the away fans' support for the entirety of the clash at the King Power Stadium.
He added: "It was unbelievable to have that support from the away fans. We know that when we lost against Crystal Palace, we felt that we didn't deserve to get beaten. However, the fans have stuck behind us and when you have two or three thousand people supporting you at an away game, that is something special.
"I had goosebumps in the first half and when we were standing in front of them at full-time. You can see the connection between the players and the fans and we really appreciate it. I'm glad they have great reasons to celebrate and hope we can give them more.
"We want to finish as high as possible but take every game step by step, looking towards a mid-table finish. We finished in tenth place last season so if it's still possible then we should try to go for it."