"I'm not vain enough to think I could come into this 350-year-old history and make things alright in a short time," he added.
Grogan said he believes the Harvard's relationship with the Cambridge city council may not indicate how residents of Cambridge feel about the University.
"For anyone in this job to keep their sanity, they have to be willing to, at some times, not define the whole of the Cambridge relationship as taking place in the city council chamber," Grogan said. "It's a particular dynamic that is not always reflective of what's going on."
But he said he believes his replacement should continue to work to improve relations with both Cambridge and Boston.
"It's in Harvard's interest to work in communities and build partnerships with them," Grogan said. "That has to continue, and I'm confident it will."