Media reports said Thursday the couple were taken to jail in Helsinki Wednesday night after an argument they were having got physical.
"Violence is not to be taken lightly. Embarrassed by drunkenness. No punches thrown, no injuries and no charges. Media always exaggerates," Lambert posted on Twitter Thursday night.
People.com said police investigated possible assault charges, but decided they weren't necessary and released Lambert and Koskinen.
Lambert said via Twitter he and Koskinen had already made up and were "laughing about it" over "hangover burgers."
Ohio bar shooting arrested, charged with murder
Duggar sisters unveil Christian dating rules in new book