For many Americans, elevated home prices have put homeownership out of reach.

They received some relief on Wednesday when the Federal Reserve cut interest rates by 50 basis points, which will lower mortgage costs. However, it's unlikely to stop home prices from continuing to rise.

Federal Reserve chair Jerome Powell said the "real issue" behind high prices in the U.S. housing market is a lack of supply, which isn't "something the Fed can really fix."

There's currently a shortage of about 4 million homes in the U.S., according to the National Association of Realtors' most recent projections. As such, the imbalance between supply and demand will continue to put upward pressure on prices.

Powell's remarks came after announcing the Fed's cut to its benchmark rate, which was based on "greater confidence" that year-over-year inflation is moving toward the central bank's target rate of 2%.

Lowering the benchmark rate to a range of 4.75% to 5% will make mortgages cheaper, potentially bringing back buyers who were previously priced out of the housing market. With rates dropping, Powell also said that "more people are likely to start moving," which could boost home sales.

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Shelter costs, which make up around a third of total spending, are still high relative to the Fed's overall target of 2%, with a year-over-year increase of 5.2% as of August, according to the Consumer Price Index.

Powell also said that shelter costs in the CPI tend to lag behind real-time prices, so the recent slowdown in home and rent prices prices isn't fully reflected yet.

While confident that housing inflation is easing, Powell said it's "not obvious" how much extra demand lower rates will generate in the housing market or the impact it will have on home prices.

The best thing the Fed can do for U.S. households is get "inflation broadly down" and reduce the cost of borrowing by "normalizing" interest rates, Powell said. Ultimately, "the supply question will have to be dealt with by the market and also by the government."

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