The result at Kingston Park on Friday took the Tigers eight points clear of the Falcons and gives them every chance of avoiding relegation.
After their away triumph, Kitchener admitted he was relieved but also sent a warning to his team-mates that there’s still work to be done.
“This win means a lot to us all…it’s the first in a little while and the manner in the way that we did it, digging in at the end, means a lot,” he told Leicester’s website.
“While we’re pleased with an away win, we can’t take our foot off the gas now.
“We’ve got a down week next week, then a big game against Bristol and we need to make sure we put our best foot forward and prepare well for that.”
Kitchener, who reached 150 Premiership matches last Friday, added that he had no idea he was set to reach such a milestone game in his career.
“I wasn’t aware, no, until I saw it mentioned on social media,” he revealed.
“It’s such a tough competition, so to get to the 150 mark is an achievement.
“Although, I’m not sure it’s one that will compute now, but when I think back one day I am sure it will feel more special of an achievement.”