Welsh singer and actor Watkins, 49, told the PA news agency he was taking the official complaint as "a massive compliment that they feel like our little festival is a little bit of a threat to their ginormous, juggernaut of a machine".
"It's a little bit mind blowing... what we're doing is very different to what they do," he added.
He also said people "love that Coachella has put Cowbridge on the map".
Watkins admitted that thousands of pounds spent on "marketing costs, posters and banners" would be "a financial impact that we have to absorb".
He added: "We've spent a lot of money on marketing and flyers and posters and banners that are all visible around the town.
"So yes, those will have to go in the bin... but let's just do that, rather than have any more people knocking on our door."
He also said there were "lots of festivals" that use wordplay, including GlastonBarry, that had not appeared to encounter the same problem.
Watkins said the idea of Moo-La-La was to "make it accessible for families that can't afford to go to Cardiff or London" for events that can cost hundreds of pounds.
"We wanted... to provide an amazing place where everybody could come have a great time, make it family friendly, accessible," he said.