Kroger was downgraded by Jefferies to hold from buy due to what it believes was a key mistake: investing in centralized fulfillment centers instead of micro-fulfillment.

Kroger should be following Walmart's lead, Jefferies analyst Christopher Mandeville added in a note Thursday.

For a grocery store chain, capturing online shoppers and catching up to Amazon-owned Whole Foods is a tricky business. Companies are grappling with how to fulfill and deliver customers' orders of fresh produce and groceries quickly and cheaply.

Mandeville said a grocery chain's fulfillment method is a make-or-break investment. It could opt for large, central warehouses, also known as centralized fulfillment, or it could go with so-called micro-fulfillment, in-store or store-adjacent spaces that are close to urban centers.

Kroger's decision to invest in centralized fulfillment centers could be a multiyear mistake, Mandeville wrote. A year after Amazon's 2017 merger with Whole Foods, Kroger signed an agreement to build 20 centralized fulfillment centers with British online grocery Ocado's robot technology.

Centralized fulfillment centers require high up-front costs. The average fulfillment center size for Ocado is 300,000 to 400,000 square feet. Each central warehouse for Kroger will cost about $55 million and take two to three years to build. A micro-fulfillment center identifies 5,000 to 20,000 square feet of underutilized space inside an existing grocery store or in a space adjacent to the current store. At both types of centers, robots perform the grocery picking.