• Walmart CEO Doug McMillon said he wants to help lower inflationary prices and won't participate "in a recession if there is one."
• The company reported fourth-quarter earnings that beat Wall Street's expectations.
• Walmart is entering its new fiscal year with caution, acknowledging the continued squeeze on consumer demand.

Walmart CEO Doug McMillon wants to help bring inflationary prices down by keeping his company's own private brands priced low, telling CNBC's Jim Cramer Tuesday that the company is "not participating in a recession if there is one."

"I think we have historically shown that we can bring prices down," said McMillon in a "Mad Money" interview.

McMillon said he would prefer that Walmart's brand partners and suppliers "step forward" on their own to lower prices, but regardless he wants "to play a role in helping get prices down."

The retail giant reported healthy holiday-quarter earnings on Tuesday as it capitalized on inflation-weary consumers looking for cheaper alternatives and discounts. The company reported record annual revenue of $611 billion.

McMillon told Cramer he was confident that Walmart's lower-priced products could push other brands to bring down their own prices, even as Walmart and its peers face rising costs.

"Over time, the market works," McMillon said. "We believe branded manufacturers and all of our suppliers of all types will have to respond to that market in time."

Walmart is proceeding with caution as it heads into the new year, issuing more conservative guidance for the current fiscal year than Wall Street expected.

"It's hard to know exactly what the back half of the year will look like," said McMillon.