Dortmund coach Edin Terzic had said earlier this month that the veteran defender was disappointed by the national team snub as his only two goals this season were winning the Champions League and participating at his home Euros.
"I can understand the idea that a group has been growing since March," Hummels told Bild Sport ahead of Saturday's Champions League final with Real Madrid.
"It's bitter for me as an individual because I'm currently one of the five best defenders in Germany. I have the self-confidence to say that."
Hummels, who has been superb in the Champions League this season, was not called up for the two friendlies in March. He said he had assured Nagelsmann back in March of his willingness to sit on the bench at the continental tournament.
Asked about the reasons behind his omission, Hummels said: "If I understood him correctly, it was more about age-related issues like fitness.
"If I'd had a phase like the one I had recently before the nomination in March (for the friendly fixtures), maybe I would have been called up - for the European Championship squad now as well."
Hummels added that most of his Dortmund team mates said "they could have easily taken you with them" after knowing Nagelsmann's decision.
Asked if 36-year-old coach had disregarded the best performers in his selection, Hummels explained it is not always about taking the best 26 players but to have a good mix who can help create a positive atmosphere.
Hosts Germany are in Group A at the Euros with Scotland, Hungary and Switzerland. They play Scotland in the tournament opener on June 14th.