The comedy has been picked up for a fourth season, but series creator Dan Harmon will not be returning as showrunner.
"Community has always been on the bubble and we decided to bring it back and see what a fourth season will do for us," Greenblatt explained at the Television Critics Association Press Tour.
"I think the fans of Community are going to get the same show that they have loved from the beginning. [But] every so often, it's time to make a change with the showrunner.
"You sort of evaluate the creative [team] and how the show is run and how the writing staff works. Sometimes you want to freshen the show. We just decided it was time to do that on Community. No disrespect to anyone."
Greenblatt also insisted that season four of Community is not necessarily the show's last, despite a shorter-than-usual 13-episode order and a move to Friday nights.
"I would love nothing more than for Community to have a following on Friday and continue," he said.
Community returns to NBC for a fourth season on Friday, October 19. In the UK, the series airs on Sony Entertainment Television.