He said it was unclear what caused the blaze, which would be investigated by fire safety officers, however he knew they were lucky to have the building still standing.
"It could have been a lot worse," he said.
The fire began in a middle section of the downstairs seating area, near a chimney, which appeared to have suffered moderate damage.
He said Mexico wouldn't be open for lunch today and said it was "unlikely" it would be able to reopen for dinner tonight.
However, he hoped to back in business as soon as possible, once the building's structural integrity and cause of the blaze had been assessed.