Werner was the hero with a second-half brace to lead visiting Leipzig to a 2-1 win over Portuguese champion Benfica in Group G.
Leipzig star Werner opened the scoring in the 69th minute before doubling the lead nine minutes later at Estadio da Luz in Lisbon, where Benfica's Haris Seferovic netted a late goal.
Afterwards, Werner hailed Nagelsmann – who arrived from Bundesliga rival Hoffenheim to replace Ralf Rangnick this season and has led Leipzig to the top of the German table after four matches.
"Nagelsmann is getting us very well-prepared before the games, he's always got a few ideas when it comes to tactics and how we can react to our opponents," Werner told DAZN. "It's worked really well in every game we've played. He sets us up, but we have to execute out on the pitch.
"It always feels great to score twice whether it's in the league or the Champions League, but tonight I think we saw phases of a very attractive game of a football. Both teams wanted to win, but for long periods our lead was deserved so we're delighted to come away with a win.
"The way my team-mates set me up today was great. That's why I'm here - to put the finishing touches on chances. Everyone put in a great performance today.
"After opening the scoring, doubling our lead was only a matter of time. We're pleased with the win, but if we can improve our chance conversion we'll be able to decide games in our favour earlier."
Leipzig defender Willi Orban added: "Nagelsmann is making every player better because we've got a little bit more structure in our game, especially with our work on the ball. You could see that in the second half - we created a lot of good situations, engineered space and that helps someone as good as Timo Werner profit up front."
It was the perfect start to Leipzig's Champions League campaign for Nagelsmann, who reportedly attracted interest from Real Madrid and Arsenal before committing to the Bundesliga outfit.
The 32 year-old sensation, who led Hoffenheim to the Champions League during his time at the club, won his first European match in charge of Leipzig and he said: "The win feels good, because we wanted to win here at the start. The victory at the start is extremely important - especially before the exhausting weeks ahead of us."
Meanwhile, Benfica assistant Nelson Verissimo said: "The game was very even in the first half, with both teams creating dangerous chances. In the second half the team that was most effective turned out to be the happy one. We had a chance before the first goal, then we had another chance for Cervi to level and we were this close from equalising after it."