Gosling, 33, hit the red carpet instead with Mad Men's Christina Hendricks, who also appears in the trippy movie, which is set in an urban wasteland.
Critical response to the film was largely negative, with Time's Richard Corliss calling it the most enthusiastically derided entry so far at this year's festival. Another critic, The Telegraph's Tim Robey, blasted it as a "crapocalypse."
Still, added Corliss, "give some credit to Gosling … for his mad mash-up of horror and social statement, crackpot fantasy and Sundance-style meandering." And Anne Thompson of Indiewire praised it as an "impressive impressionistic well-wrought debut."
Meanwhile, Mendes, 40, has been keeping a low-profile, and the pair haven't been photographed together since last November. But in February Mendes appeared to playfully shoot down breakup rumors, telling Ellen DeGeneres that her Valentine's Day plans involved "watching The Notebook or something."
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And in May Gosling was photographed at the premiere of White Shadows wearing a necklace reading "Hugo" – the name of Mendes's beloved dog.
As for his new film, in an interview with the official Cannes site, Gosling said Lost River was influenced by "'80s and early '90s cinema."
And despite the critical drubbing, he said he's at work on another script.
"I'm writing a comedy," he said. "So far it's not very funny, so I'm working on that."