The only means for retailers to compete with Amazon.com (AMZN) - Get Report is to "bite the bullet" and copy Amazon with a "radical rethinking" of how they add value for customers, AlixPartners said in a note.

Even as overall retail sales remained relatively flat in June, Amazon continued to dominate. With its recent Whole Foods Market (WFM) acquisition, Prime Wardrobe rollout and sales record on Prime Day, Amazon will outdo all competition.

Retail boards and CEOs who call their categories "Amazon-proof" are "laughable," and out-competing the retail giant is never going to work, AlixPartners said. But doubling down on analytics, insight and value-adding features can help retailers keep pace with Jeff Bezos' behemoth.

"Amazon will never stop innovating and taking risks," AlixPartners said. The company constantly finds new ways to add value for customers, from loyalty rewards to easy returns. Staying on par with Amazon in at least a few value-adding and analytics services is the only way for retailers to "stop the bleeding of customers."

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