Taime Downe‘s speaking out about his fiancée’s fatal fall from a cruise ship balcony … placing the blame squarely on addiction.

The Faster Pussycat singer spoke out on “Trunk Nation with Eddie Trunk” — a SiriusXM show — last week in his first public comments since his partner, Kimberly Burch, fell off an ’80s-themed Royal Caribbean Cruise.

Downe tells Trunk he’s obviously heartbroken over the death of his partner … and, he calls her death “alcohol and prescription-related.” He doesn’t elaborate on what he means here — but, it seems he’s suggesting Burch may have been intoxicated.

We broke the story … Kimberly fell from the ship back in March shortly after an argument with Downe. Burch’s mother, Carnell, said she didn’t think her daughter would hurt herself, but admitted she was drinking on the cruise prior to her death.

Sources with direct knowledge told us … the Miami-Dade Sheriff’s Office in Florida is in possession of video that shows Kimberly climbing the ship’s rail and taking a step off.

Taime’s moving forward despite his grief … ’cause he and the rest of Faster Pussycat are touring right now. They have three shows in Texas this week before they head to the Midwest.