The sad tune contains the lyrics, "He could have your humor, but I don't understand / 'Cause he'll never love you like I can, can, can."
He also posted this telling shot on Instagram on Tuesday, in which he pouts with a glass of red wine.
"Sometimes you just need to lay in bed with a glass of red wine and a football T shirt and listen to Joni Mitchell," he wrote. "It's been a sad day. Beautiful show, but sad day x."
Ironically, Smith actually met Zeisel when the model was an extra on the New York City set of his black-and-white music video for "Like I Can."
"It's very early days," the "Stay with Me" singer told The Sun in December. "I'm talking very, very, very early days. But he's really sweet. I met him on the video for 'Like I Can,' he was one of 20 extras."
He later posted pics of him and his new beau during a trip to Sydney, including the two recreating Jack and Rose's famous Titanic pose on a boat.
Smith got into a bit of trouble in October, when he tweeted that he was too sick to meet fans after a Nashville show, but was later caught on camera having a karaoke session to Beyonce's "Flawless" the same night.