The animal welfare charity received a call with concerns for the welfare of the pony, after she was found in Moor Park Lane on Sunday, January 19.
The young pony, who was underweight and had diarrhoea, was taken for urgent veterinary care, but had to be put to sleep after her health continued to deteriorate.
RSPCA chief inspector, Rob Jackson, encouraged people with information to assist the investigation.
“We would really like to hear from anyone who knows who left her there. She needed help, not abandonment," Mr Jackson said.
"Whoever did this cut through a padlock before abandoning her when she was clearly in need of urgent veterinary care.
“Sadly situations such as this are not uncommon and we see far too many incidents involving horses who have been left in this way. The RSPCA and other welfare charities often deal with ongoing welfare issues involving abandoned and fly grazing horses.
“Anyone with information can contact the RSPCA appeal line on 0300 123 8018.”