New Zealand Post announced it would close the branch in the Exchange earlier this month due to a lack of customers.
Mr Cull said on Friday he had received calls by email to back opposition to the closure of the branch, suggesting the mayor and councillors should be "jumping up and down" about the issue.
"I'm not sure that is our job, nonetheless, as it is a commercial operation," Mr Cull said.
Mr Cull said his take on the issue was that he had used the post office for the last 10 years, as he had a post office box there.
"My first observation is that the staff have been fantastic," he said.
But he had noticed the number of customers who used the facility had declined over the decade, as much of the business had become web based.
"It's quite empty," he said of the branch.
It was up to management of the branch to decide whether it was commercial or not.
Save Dunedin Metro Post Shop and Kiwibank campaign spokesman Victor Billot said the mayor was out of touch with local people, as about 2000 people had signed a petition to keep it open.
"The mayor does not realise the importance of Dunedin metro to local businesses who are regenerating the Exchange area, or the nearby hotels who will host visitors to the city later this year."
Otago Chamber of Commerce chief executive John Christie said many of the chamber's members in the area were upset about losing the service in the area.
"It will be a big loss for frequent users."
