Nagelsmann says thumping of Scotland a 'first step'
Germany, who have struggled at major tournaments for most of the past decade, blew the Scots off the park.
"The team is conscious that this was a first step," said Nagelsmann as Germany eye a record-breaking fourth European title.
"But it was very good and very important and was something that we can build on."
Germany opened the scoring just 10 minutes in through Florian Wirtz, with man-of-the-match Jamal Musiala adding another on the 19-minute mark.
Kai Havertz scored from the penalty spot to give Germany a 3-0 half-time lead after Ryan Porteous received a straight red for a studs-up challenge on Germany captain Ilkay Gundogan.
Niclas Fuellkrug and Emre Can then both added second-half goals.
The coach said he "would have signed on the dotted line" before the match to guarantee his side performed like they did on Friday, "even if I didn't expect it".
Nagelsmann, who only took over as Germany manager in September, said he was particularly pleased by his side's reaction to conceding a late goal while 4-0 up.
"We didn't let in any chances from open play. It was a very good sign for the team to be so pissed off that we conceded that goal.
"That shows the hunger that they had today."
Havertz said his team had laid down a marker to the rest of the teams in Germany for the tournament.
"I think that when you win 5-1, it's a message. But it's just the beginning.
"We saw the quality we have in the team, how good the players are. We're going to come up against other difficult opponents."
Having set up Musiala's goal and converted a penalty, Havertz now has four goals in his past seven Germany matches.
"I think we felt this energy in the stadium from the first minute," the 21-year-old said.
"The whole country is behind us, we saw it at the training centre. We're aware of it."