Mr Huggins says he believes the cost of living crisis is pushing people to abandon the animals.
But he says it is impossible to point to one single reason behind the issue as each goat's story is different.
Some dropped off at Buttercups were taken on as pets but the owners found them too difficult to look after, or they lost interest, he said.
Others, meanwhile, were recovered by the police dumped on the side of the road or "thrown over" the site's gate, Mr Huggins said.
Mr Higgins, who has worked at the shelter since 2013, said: "Goats are very clever. They need lots of stimulation otherwise they get up to mischief quite quickly.
"But they are a lot of fun," Mr Huggins continued.
"Goats are great if you put in the time and effort with them. They are full of personality."
To help the sanctuary, he is urging people to consider rescuing a goat, but only if they do their research and are prepared to commit.
Buttercups, which is funded entirely by donations, is also appealing for financial help from the public to look after the goats.
Mr Huggins estimates the shelter costs £1,000 per day to run.
"Thankfully, we are here," he added.
"I don't think anyone thinks... there would be such need for a facility like this because goats are such a random animal.
"But when you scratch below the surface, they are everywhere."