Stitch Fix is finding success in an evolving retail landscape because its business embodies the new consumer preference, CEO Katrina Lake told CNBC on Tuesday.

"Today people want to be treated like unique individuals and they want to be respected for their preferences," Lake said on "Squawk Alley." "And I think our model is really well suited to deliver against that."

Investors on Tuesday, at least, were buying into the Stitch Fix story. Shares of the clothing styling service closed up nearly 5% to just above $26 on Tuesday after its quarterly results, which were released after the bell on Monday, eclipsed expectations.

The company, which went public in November 2017, turned in a breakeven quarter as analysts had forecast a loss of 6 cents per share. Revenue grew 21% year over year to $445 million, above the $441 million that had been expected.

Stitch Fix's active clients matched analyst estimates at 3.4 million, a 17% increase from a year earlier.

In addition to the overall number of subscribers increasing, Stitch Fix also saw growth in the amount of money existing clients were spending — with revenue per client rising 10%.

That means clients are "buying more things, staying longer, having more successful experiences, and that is all great," she said.

The way in which subscribers can experience Stitch Fix also is changing, Lake noted. Traditionally, Stitch Fix sent customers five items, chosen by a personalized stylist. Customers pay for the items they want to keep.

But in October, Stitch Fox began rolling out a new service called Shop Your Look, which shows subscribers around 30 to 40 items, utilizing data from their previous purchases, and gives them a chance to buy products individually.

"It's a very radically different e-commerce experience," said Lake, who founded Stitch Fix in 2011.

So far, Shop Your Looks is available to only 30% of Stitch Fix's women's clients, Lake said, "so we have a lot of work to do to optimize the feature" and make it available to its millions of subscribers.

Lake said she didn't think Shop Your Looks cuts into the business of Stitch Fix's traditional five-item boxes. Rather, she said it is "additive" and opens the door to further evolution of its business model, including expanding into holiday gifts, for example.

"The market opportunity for a more personalized apparel buying experience is enormous," said Lake, who contended that the days of retailers saying, "This is the 'it' thing and everybody should go buy it, are gone."

One area that Stitch Fix will not be experimenting with anytime soon, Lake said, is brick-and-mortar retail.

While some formerly online-only retailers such as Everlane have jumped into the world of physical stores, Lake said Stitch Fix hasn't ruled it out but "we don't have any plans in the near future to do that now."