The Premier League outfit were 2-0 inside the first 30 minutes but surged back into the contest and took the lead through goals from Alexis Mac Allister (two), Ronald Araujo and Florian Wirtz.
Villarreal found the back of the net late, but it proved a mere consolation as the Reds held on to take maximum points.
In quotes published on the Liverpool website, Nyoni said: "There was no panic at all. Everyone believes in each other and I feel like when the team morale is like this, none of us can panic and we believe in our quality.
"You saw in the second half how we changed the game and upped the tempo a bit more, which is what we needed to do. And scored the goals."
It was a first start in Europe's elite competition for the 19-year-old Nyoni, and the teenager was grateful to be given the responsibility while learning form his more experienced teammates.
He added: "It's special. I've had to wait but I feel like it's all part of the process. I've learned a lot over the last few years, even just being on the sideline watching the rest.
"My teammates help me, especially the senior players, they help me a lot when I'm on the pitch and they try to make my job as easy as possible. I can't ask for more."
Former Kaizer Chiefs defender Aden McCarthy believes his maiden UEFA Champions League goal can serve as the foundation for a successful spell in European football after finding the net against Borussia Dortmund.
Liverpool defeated Villarreal 4-3 in their UEFA Champions League encounter at Anfield on Tuesday evening to maintain their perfect record in the tournament.
Aden McCarthy netted his maiden goal in the UEFA Champions League but it was not enough for his team Sabah as they fell to a 2-1 home defeat against Borussia Dortmund in Baku.
Liverpool boss Andoni Iraola has revealed that Villarreal counterpart Inigo Perez was his preferred choice to join his coaching staff before a work permit rejection prevented the Spaniard from moving to Bournemouth in 2023.
