Germany qualified for a record 13th European Championship with a 4-0 defeat of Belarus in Monchengladbach on Sunday (AEDT).
Matthias Ginter broke the deadlock at the end of a frustrating first half, before Leon Goretzka doubled the hosts' lead and then Kroos struck twice.
The scoreline belied some of the difficulties the 2014 world champion faced, reliant on Manuel Neuer to make three fine saves, including an Igor Stasevich penalty.
Joachim Low has disposed of a number of senior men since a poor 2018 FIFA World Cup, and Kroos, one of the remaining established stars, sees there is work to do for a young group.
"We are still lacking a little bit in experience, but certain procedures are working better and better," he said.
"We will know where we stand shortly before the tournament. Currently, I would not count us amongst the top favourites. But that doesn't always mean anything."
Like Kroos and Neuer, Ginter was central to the victory, having a hand in the second and third goals after scoring the opener at Borussia-Park, the home of club side Borussia Monchengladbach.
The smart flick was Ginter's first strike for his country, prompting comment from Neuer that it was "about time".
"His first Germany goal tonight? Well, after 29 games, it is about time," Neuer said. "No, he did very well to score in style."
Ginter added: "Scoring a goal like this as a central defender - that goes to show that nothing is impossible. Manu is right - after 29 games, it was about time.
"Scoring here in Gladbach is the icing on the cake."