People living around Ecclesall Road will have to pick up their parcels from Pond Street in the city centre when the Sheffield South West delivery office shuts on July 4.
The decision to close the Ecclesall office was made despite a campaign to save it, which attracted thousands of signatures on a petition.
Royal Mail said it was responding to a decline the number of letters posted. But Steph Gale, who started the campaign against the closure, said the company had not listened to customers.
“It’s disappointing but inevitable,” she said. “There was no consultation with the public. They didn’t respond to the petition or the comments.”
Opening hours at the Pond Street office, two-and-a-half miles away, will be extended to allow Ecclesall customers to pick up their parcels. But Mrs Gale said this would not still not be convenient.
“People are very adaptable and we have to adapt, but I don’t think what they have offered is acceptable.
“They have extended the opening hours but it’s really hard to get down to town and it’s still basically office hours.”
City councillors and Sheffield Hallam MP Nick Clegg were among those to join the campaign.
Mr Clegg said: ““It’s a real shame the Royal Mail have refused to listen to the community and pressed ahead with the closure of the South West sorting office. I am calling on the Royal Mail to think again.
“I will be writing again to the Royal Mail to let them know my opposition to their decision.”
Coun Shaffaq Mohammed, who also backed the campaign, said: “It will mean people now have to go to Pond Street, which means added inconvenience, traffic and congestion.
“We got 3,000 signatures on a petition. We could probably have got more.
“I just wanted to show Royal Mail that people were telling me the office was an integral part of the community. They have gone away and decided that they are closing it.”
Labour members in Ecclesall also campaigned to save the office. Chairman of the Hallam Labour Party Andy Belfield said: “I’m really proud of the campaign that Labour and people in Ecclesall ran to save our parcel office. People signed petitions, put up posters and tried to make a difference. That has led to a commitment to Labour that local collection will still be provided. It’s disappointing that the office is still set to close but at least that important local service is to remain.”
A Royal Mail spokesman said the changes would help deliver the most ‘efficient, consistent and reliable’ service to customers and help secure long term employment and job security.
There will be no job losses as a result of the closure. The firm said deliveries would not be affected.