"Yeah right," Pattinson replied, to which Kravitz admitted: "Sorry, not my thing."
"It's not even cool to be a hater anymore," the 35-year-old who plays Batman, aka Bruce Wayne quipped.
"I don't hate it, I just didn't see it, I just didn't participate in it," the 33-year-old who plays Catwoman, aka Selina Kyle, explained as Pattinson jokingly described her opinion as "so 2010."
Though Kravitz later recalled that she had actually watched the first Twilight film with one of her best friends, although the actor said "...she kind of made me go [to see it] so I don't really remember it."
The Batman is set to be released in UK cinemas on March 4, with the London premiere of the film taking place last night (February 23).
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