Frenchman Varane made his first start this season alongside new recruit Lisandro Martinez (24) with Ten Hag's decision to drop captain Harry Maguire (29) paying off as the home side won 2-1 at Old Trafford after starting the season with two losses.
United looked a completely different side to the one that lost at home to Brighton & Hove Albion and were thrashed at Brentford as they created numerous chances and Varane said he hoped the result was a launchpad for the rest of the season.
"Football, it's about energy, it's about when you have to push, when you have to stay calm, when you have to attack. We showed a great control. It was a mature performance," the former Real Madrid defender told reporters.
"I really enjoyed it on the pitch, the atmosphere, the spirit of the team. I came to England to feel these emotions after everything I left in Madrid.
"This feeling was amazing, absolutely amazing - the crowd, the fans and the fight on the pitch. It's difficult to explain why, but we didn't start the other games with the same intensity, the same fighting spirit."
Varane said he hoped to build on his first start after enduring an injury-ridden, stop-start campaign in his debut season following his move from Real last year.
"I feel very good. I was ready for the start of the season but I didn't start so I had more time to keep building fitness," the 29-year-old added.
"I have demonstrated in the past what I can do when I'm fit, so that's my focus for this season. I really want to help the team. Some moments in the last season were frustrating, I know I need to be fit to enjoy (it)."
Check out all of the statistics from United's win against Liverpool with Flashscore.
