Curry departed the show last month after 15 years. The exit came just one year after she made her debut as co-anchor alongside Matt Lauer.
Greenblatt has since said that Curry's departure, which made way for Savannah Guthrie to take the job, was necessary to ensure that Today remains successful.
"I will say that to be number one for, I don't know, 16 years or something, as that show has been, shows go through transitions and they're always difficult," Greenblatt told reporters at a Television Critics Association press conference on Tuesday.
"I think everybody in the news division from what I could tell took as much care as they could... to make this transition happen.
"It's never easy. Things leak and you try to do things respectfully and then you have to go out and announce something you weren't ready to announce. My heart goes out to all those people, including Ann, and everybody who went through that transition."
It was recently reported that Lauer supported Curry's exit from the programme.