Cal Ejike, 45, was trying to use the cash machine outside the shop, but when there was no cash available he went inside to use the Post Office instead.
He said: “I use the Post Office for the foreign money exchange and getting insurance. It’s not good that it’s closing. It’s a part of the local community. Elderly people like to use it.
“I don’t think it’s a good idea to close it. It used to be an ever-presence in the community – just like high street banks. All these closures are affecting our community.”
Bricknell Ward councillor Sharon Hoffman said the aim of the petition was to ensure the Post Office “doesn’t forget about us”.
She said: “It’s an absolutely vital service. Many, many people use it, including myself as I’m a resident of the Bricknell ward, and I’ve had a number of residents, since I’ve found out the service is closing, really concerned.
“A number of our residents have limited mobility, and lots of them don’t drive, older people particularly, and the next nearest post office is quite a way away for them. They’ve said it’s going to be really difficult for them.”
Hoffman said residents were “really desperate” to retain a Post Office branch.
According to a poster in the shop window, the nearest two branches are in Chanterlands Avenue and Inglemire Lane, 1.1 miles (1.8km) miles and 1.2 (1.9km) miles away, respectively.