The girl, who has not been named, was taken to the Princess of Wales Hospital, where she later died.
Local councillor Peter Foley said: "It's a great tragedy. I don't blame the kids for playing here. They should be safe here."
Police say a full investigation is being carried out, next of kin are being informed and a file is being prepared for the coroner.
The waist-high black metal gate is at the entrance to a small car park at a three-storey apartment building about five minutes walk from the town centre.
Residents at the modern block of privately-owned flats, which is surrounded by streets of terraced houses, said the accident happened about 1700 BST on Saturday.
The little girl, who lived nearby, was understood to be eastern European.
Eleanor Jones, who lives opposite the scene, said a large number of police officers were in the street when she returned home about 1830 BST.
She said: "I can't believe it because the little girl was there when I went out.
'Floral tributes have been left at the scene'
"By the time I came home it was just police in the street. I had seen her but I didn't know her."
She added: "It's devastating. You can't believe that a gate would do that."
The gate was open and de-activated following the incident.
Floral tributes, teddies and cards were left on the railings outside the apartment block.
One read: "Tears are in my eyes when I think about a beautiful little girl lost."
Another said: "Pedal your little bike as fast as you can to heaven. Sleep tight little angel."
The accident follows the death in Manchester last Monday of a six-year-old crushed by an electronic gate.
Semelia Campbell was playing with a friend near her home in Moss Side when the motorised gate closed on her.
The schoolgirl was eventually freed when police broke off an electronic box.
She was rushed to Manchester Royal Infirmary but died from her injuries a short time later.