Curry was fired from the NBC show and replaced by Savannah Guthrie in the network's effort to improve the program's falling ratings.
Although Lauer has been widely criticized as being responsible for Curry's firing, he told The Daily Beast he actually told NBC Universal chief executive Steve Burke he would "get out of the way" if Burke thought "Today" was better off without him.
However, Burke told the website he declined Lauer's offer because he is "the best person who's ever done this."
Lauer admitted he and Curry didn't have great chemistry, but he also said he objected to her outright firing.
"I don't think the show and the network handled the transition well. You don't have to be Einstein to know that," Lauer told The Daily Beast. "It clearly did not help us. We were seen as a family, and we didn't handle a family matter well."