Speaking at the International Coaches' Congress in Mainz, where Völler stood in after Klopp withdrew from his scheduled address, Völler said Nagelsmann had ultimately lost the public backing he needed to continue.
"Many people here know Jürgen and know that he has the ability to carry people along with him — players, his coaching staff, employees, and of course the fans too. Especially in difficult situations, he has the quality of winning people over. That became harder for Julian Nagelsmann at some point. He no longer had the backing in the media or among fans that he would have needed," Völler said.
The sporting director went on to defend Nagelsmann against what he felt was excessive criticism during his tenure.
"I found the criticism from many experts at times unfair and often too harsh. With Julian, at some point almost every decision was fundamentally judged negatively," he said.
Völler also revealed he had personally come close to resigning after Germany's exit from the World Cup, which ended in a shock defeat to Paraguay.
"Of course I thought about stepping down. But I asked myself whether it really made sense to throw everything away now," he said.
Turning to his working relationship with Klopp, Völler indicated a lighter touch than he had taken with previous coaches.
"Certainly not supervise or accompany him the way I might have done with other coaches. That's not necessary anyway," he said. Klopp officially takes over as head coach on 15 August, with his first fixture in charge coming in Nations League action later that month.
Klopp himself addressed the congress only via a pre-recorded video message, explaining he did not want to "make headlines again right at the start" before having taken charge of a single match. He is expected to deliver his planned address to the Bund Deutscher Fußball-Lehrer at a later date.