When police arrived, Mike said they tied the goats to a pole before sorting out the man. Police then used the man's leash to take the goats away.
Many on social media came up with clever puns to describe the incident.
"I think you might be jumping to conclusions - it could be a frame-up ... they might be scapegoats," one person hilariously wrote.
"You're kidding, right?", someone sarcastically asked, playing on the fact young goats are called kids.
"How dare ewe," another person responded.
One person came up with a "punny" headline: "Cop saves three kids from drowning."
A police spokesperson told the Herald that they "received a report of an intoxicated man lying on the ground on Auckland St in Picton about 2.10pm on Sunday, 6 January."
"There were four goats with the man. Police attended and took him into custody to detox."
However, the spokesperson had no information about what happened with the goats.