's (NASDAQ:AMZN) rise to fame as one of the world's largest online retailers left brick-and-mortar chains scrambling to catch up. Big-box retailers are no longer the only ones feeling pressure from the consumer shift to online shopping. Today, the wrath of the e-commerce revolution has descended on luxury retailers.

New research from Deloitte suggests that luxury brands are losing their exclusivity appeal as more consumers choose to shop online. This could be a problem for high-end brands such as Tiffany (NYSE:TIF) and Burberry, both of which are notorious for refusing to discount their merchandise.

The cult of online couture
Luxury designers have traditionally relied on exclusivity as a means to charge premium prices for luxury goods. However, thanks to the Internet, consumers now have access to more information and options when it comes to shopping for high-end brand-name products. This has made it easier than ever for consumers to comparison shop online for the best prices, thereby creating serious challenges for discount-averse luxury retailers.

It's no secret, for example, that Tory Burch seldom discounts its merchandise. However, an Internet-savvy consumer can now get top designer products from Tory Burch and others on flash-sale site MyHabit for up to 60% off. What's more, MyHabit and other top fashion sites including Shopbop and Zappos Couture are all owned by... drumroll... Amazon.

Because the e-commerce giant already has a robust logistics operation, Amazon is able to further sweeten the deal for consumers by offering free shipping on most purchases at these luxe fashion sites. As a result, fashion is now Amazon's fastest growing business. 

Source: Amazon.

Amazon's budding fashion business is a great example of how e-commerce is changing the rules for luxury retailers today. Consumers now care more about value than ever before, due in large part to the price transparency afforded by shopping online. This also makes it more difficult for luxury brands to maintain their high-end reputations.

Moreover, in an apparent attempt to preserve their brand image, some luxury retail companies today are choosing to offer only a highly curated selection of products on their respective websites. While this is one way to maintain strict control of the brand, it detracts from the convenient nature of online shopping.

E-commerce is an unstoppable force
Of course, there are still iconic brands, such as Chanel, that refuse to sell merchandise online for fear of cannibalizing physical retail locations and losing their exclusivity appeal. Yet the overall U.S. e-commerce market continues to grow rapidly, reaching more than $703 billion in 2013, according to Statista. 

You would think this would be a wake-up call for luxury brands that don't yet have compelling online offerings. However, last year, an astounding 40% of luxury brands still didn't sell merchandise online, according to estimates from consultancy firm Bain. Amazon's fashion business, meanwhile, is only five years old and already boasts more than 40 million customers. 

Being fashionably late to the e-commerce table could spell trouble for luxury brands if they're unable to find a work-around for the price transparency issue. A quick online search, for example, led me to find Tiffany & Co.'s Adagio sunglasses on for nearly half the price that they were selling for on Tiffany's e-commerce platform. For most customers, this makes shopping on Amazon a no-brainer.

To be clear, consumers haven't lost their appetite for luxury products. The difference now is that consumers favor value over exclusivity when it comes to luxury items -- and retailers like Tiffany have online shopping to thank for this.

Ultimately, rich profit margins will only take luxury retailers so far. An estimated 78% of the U.S. population age 15 and older shopped online during the first quarter of 2014, according to BI Intelligence. And that figure is growing at a rapid clip today.

This means luxury brands need to find innovative ways to connect with consumers where they are shopping -- online -- without diluting their brands. Not only would it help these brands avoid alienating their affluent Internet-savvy customers, but it would also expose them to so-called omnichannel shoppers, who tend to spend as much as 76% more than in-store-only shoppers, according to Deloitte. 

As for investors, retailers with strong e-commerce and mobile platforms will likely dominate going forward as consumers spend more time shopping from the comfort of their living rooms.

Aside from Amazon, investors should keep an eye on Kate Spade (NYSE:KATE). Traffic to the luxury retailer's Japanese website climbed an impressive 80% last year. This, along with new e-commerce markets such as the U.K. contributed to international sales growth of more than 46% in fiscal 2014. Moreover, Kate Spade plans to keep the momentum alive by launching new sites in other markets, including France, in the months ahead.