Colleen Tinnelly of the charity said the abandoned puppy was “just not strong enough” to survive.
“Unfortunately, it is very sad to say that one of them passed away last night (Thursday),” she said.
“Our vet team worked tirelessly around the clock yesterday at the USPCA and it was probably one of the most heartbreaking I have ever had in this job – watching our staff try to keep one of these puppies alive.
“The other four are doing very well, but this is only the beginning.
“They are very, very young and they have been taken away from their mother, but they are happily doing well and we hope they make a full recovery.”
The litter is one of many cases of animal abandonment reported by the USPCA when it reopened on Wednesday after the Christmas holidays.
Ms Tinnelly said: “This is the worst year I have seen. We are under great pressure with restrictions and the number of volunteers and staff on leave with Covid per minute
“So we find it really difficult. We have had the busiest two days I have seen in a long time.
Other animal shelters across Northern Ireland are said to be operating at full capacity.
Speaking on Thursday, Ms Tinnelly said: “Unfortunately, in the months after Christmas we are bracing for an increase in the number of unwanted animals and trying to accommodate as many as possible.
“Never have we seen cases like this so quickly behind Christmas. We are shocked and very disappointed that this continues to happen.
She added, “Our advice on responsible pet ownership is clear: an animal is not a toy.
“It is a lifetime commitment and does not come with a return policy.”
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