The campaign group Stand Up to Racism claimed a brick was thrown through the window of the Cladhan Hotel on Monday night.
The hotel has been the site of a number of protests, with some activists urging the UK Government to shut the facility.
Speaking at a press conference in Edinburgh on Wednesday, John Swinney said: “I absolutely deprecate the throwing of a brick at the window of the hotel.
“I think it’s absolutely despicable that should have happened.
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“There are people inside that hotel who have experienced fear and terror and I’m appalled that they’re experiencing fear and terror in Scotland, our country.”
On the protests more widely, the First Minister said he had seen some “terrible language” used on banners.
“Absolutely appalling language about people, fellow human beings, and that is designed to create some fear and alarm,” he said.
Anti-racism group Falkirk For All described the attack as an “act of intimidation” and said it was “unacceptable”.
A spokesperson for the group added: “Rising anti-immigration rhetoric is fuelling hostility and creating an environment where such actions take place. Everyone has the right to feel safe in our community, and actions like this bring our town into disrepute.
“If you truly believe in community safety and what is best for Falkirk, then you should do more than just distance yourself from such actions.
“We call upon Save Our Future & Our Kids Futures (which has organised protests in Falkirk) to publicly condemn this act of violence. To remain silent is to endorse attacks that impact local workers, staff, and residents, and encourages further anti-social behaviour in our town.
“Falkirk should not, and does not, tolerate these targeted attacks against our community. Our town is an inclusive, diverse place and there is no room for division and racism here.”
