The Germans, who were struggling with injuries leading up to October's Nations League matches, emerged victorious thanks to a brilliant second-half goal from newcomer Jamie Leweling.
“The first half tonight was the best we’ve played this year,” Nagelsmann said, adding that “the greed that the team embodied was a huge step”.
“We did well and let very little in. We absolutely deserved to win.”
Germany qualified for the Nations League knockout round for the first time with the win and the coach also said that his team were fired up to go further.
“We’ve got the ambition to keep going. There’s a supercharged atmosphere in the dressing room – they want to win,” he said.
Germany made seven changes to their squad in the lead-up, with injuries to key players including Jamal Musiala, Kai Havertz and goalkeeper Marc-Andre Ter Stegen.
Deniz Undav, who scored a brace in the 2-1 win over Bosnia on Oct 11, was ruled out after an injury in the warm-up, giving Leweling his debut.
The Stuttgart forward had an early goal ruled out for the tightest of offsides before blasting in a loose ball from a Joshua Kimmich corner.
A beaming Leweling told Germany’s ZDF network: “We won as a team, I scored the 1-0, we won 1-0, but we did well and I’m just happy I could help out.
“The Dutch are a top nation, but we played a good game nevertheless. We used the chances that we had well.”
Nagelsmann said that Leweling “surprised” him, adding: “I didn’t expect him to play so well.”
The 37-year-old’s first game in charge was a 3-1 win over the United States away from home on Oct 14, 2023.
He was appointed after predecessor Hansi Flick became the first coach in German history to be sacked from the top job, with the proud football nation flailing due to a series of poor results.
The victory was Germany’s 10th win in 17 games under Nagelsmann. The side’s only loss since the start of 2024 was in extra time in the quarter-finals of the European Championship on home soil against eventual champions Spain.
Germany captain Kimmich, who was part of the side’s disappointing group-stage exits at the 2018 and 2022 World Cups, told reporters that “you can tell everyone’s up for it”.
“Everyone standing on the field has the desire to play, has the desire to win,” he said.
“I think you could tell from outside that we had the desire to play football and the drive to defend.”
He also said the side were proud to overcome a long injury list.
“We had lots of new players, some young players, unfortunately lots of injuries but you didn’t notice much of a difference,” he added.
“Jamie had an outstanding debut – it’s not often the Allianz Arena gives you a reception like that – he did well.”
Dutch stand-in captain Stefan de Vrij, meanwhile, said that “this wasn’t the game we wanted”.
“We know Germany have a very strong team. We have to analyse and improve,” he said.
“We’re confident about our Nations League chances. Next month will be crucial, especially the first game against Hungary, but we will stay positive and try and win those games.”
The Netherlands, missing suspended captain Virgil van Dijk, were poor until the dying stages. They stayed second in the group but only on goal difference ahead of Hungary, who beat Bosnia 2-0.
Before the match, the hosts bid farewell to international veterans Manuel Neuer, Thomas Muller, Ilkay Gundogan and Toni Kroos, who have all stepped down since the home Euro in the summer. AFP,