Some prices have begun to fall after inflation reached an all-time high, but those hoping for a major reprieve when it comes to consistently needed goods like groceries shouldn't hope for relief anytime soon, at least according to the CEO of Walmart.

Speaking to CNBC, the company's CEO, Doug McMillion shared that despite some slowing on inflation, groceries and other essentials are likely still going to be causing some pressure when it comes to consumers' wallets. While the November Consumer Price Index did show that prices rose 7.1% year over year, which was below estimates, food prices are still elevated at 10.5% year over year—and it likely isn't going to change anytime soon.

Because grocery items are shipped more frequently than other merchandise because of demand, and trucking prices are also elevated, prices aren't likely to see a big drop soon.

"What we're seeing is that if you take the fresh food categories, commodities, things like proteins, things are starting to move. Chicken right now is more expensive, but beef is down. Fruit and vegetable is in pretty good shape," McMillon said. "But dry groceries, consumables is where we're seeing the most stubborn and persistent inflation, mid double-digit inflation. And we're not hearing from our suppliers looking forwards that's going to come down soon."

"We think there's going to be persistent inflation with us for a while, in drug, grocery and consumables," he added.

However, McMillon did share that Walmart is remaining hopeful that they can provide some relief to customers over time, and that they are monitoring things as they progress, with the intention of eventually adjusting prices when possible.

"We're managing this item by item, category by category," he said. "We have a plan and adjusted our inventory to be ready for this next year."

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Michael Lipsitz does his grocery shopping at the WalMart in Crossville, Tennessee March 21, 2008. Reuters
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