For example, Walmart recently paid $16 billion to buy a majority stake in Indian e-commerce company Flipkart. In late 2016, it paid $3 billion for then-startup Jet.com.
Amazon "certainly wouldn't have grown to the scale it is, and they wouldn't have got the lead they have" if Walmart had gotten an earlier start, said Storch, former CEO of Saks Fifth Avenue-parent Hudson's Bay.
Walmart does draw "strength" from leveraging its brick-and-mortar stores to compliment its e-commerce operations such as its online grocery ordering and in-store pickup, he said. "That is the model of the future."
Storch appeared on CNBC Thursday just hours after Walmart reported mixed third quarter results.
While revenue fell short of estimates, Walmart earnings beat expectations, fueled by strong e-commerce sales. Online sales were up 43 percent during the quarter.
Walmart also raised full-year forecasts and predicted a strong holiday shopping season.
Brett Biggs, chief financial officer at Walmart, told CNBC the company was still on track to meet its goal of 40 percent e-commerce sales growth for the full year.
Amazon, on the other hand, is growing 20 percent a year "on a much larger base," said Storch, former chairman and CEO at Toys "R" Us.
Walmart has a stock market value of about $290 billion. Shares, while lower Thursday, were still up about 11 percent year-to-date.
Shares of Amazon, which fell into a bear market earlier this week, has a market value of about $760 billion. Amazon had become the second company behind Apple to hit a $1 trillion market cap on Sept. 4. Despite the recent sharp drop, the stock was still up about 35 percent in 2018.