"What put me onto this was that one of them was calling frantically for her baby, couldn't find it," Casto said. "I did a head count, and two were missing."
Casto told CBS Denver that he felt "anger and sadness" after realizing that the goats were missing, adding that "they're nicer than humans."
"I feel sadness in my life. My wife is heartbroken," he said.
He also feared for the lives of the baby goats, who he said must be bottle fed about four times a day.
"They're like infants. They need to be fed every few hours," Casto said.
According to Casto, there was no sign that a coyote broke onto the farm, but he noticed a fence in the wrong position near where he had seen a red pickup truck driving by earlier in the week.
"I thought it was just a sightseer, but now I wish I had gotten the license plate number," he said.
Casto hopes that the $1,000 reward will inspire the culprits to return the baby goats if they were stolen as part of a prank.
"If it is kids who did it, then there are probably other kids who know who it was. At least one of them could use $1,000," he said.
