Most millennials, 66%, don't feel on track when it comes to saving for retirement. That's according to a 2019 TD Ameritrade report, which surveyed 1,015 U.S. adults aged 23 and older with at least $10,000 in investable assets.

When asked why they've fallen behind on their retirement savings, the No. 1 response for millennials (ages 23 to 38), was housing costs: 37% cited it.

Partly because of rising rental prices, young people are spending big chunks of their income on housing. That's especially true for families: 1 in 5 millennial parents reported spending 50-59% of their income on housing, according to a 2016 report from the National Endowment for Financial Education and Parents magazine. And 8% said they're paying 60-74%.

It doesn't leave much room for savings. As a rule of thumb, money experts recommend putting half of your take-home pay toward necessities, which includes things like housing, transportation, food, insurance and childcare. About 30% of your income can go toward "fun" and the remaining 20% should go toward savings for your future self.

Besides housing, 33% of millennials say that "supporting family members financially" has prevented them from saving enough for retirement. And 26% cite "inadequate income" for causing them to fall behind.

About one-fifth (21%) of millennials say that student debt is holding them back from saving for their future. This is a much more common answer among young people: Only 12% of Gen Xers and 5% of boomers feel this way.

The good news is, there are ways to save on housing and free up more room in your budget for retirement savings. Here are three strategies:

When shopping for a place, make sure you're not getting more than what you need, recommends one millennial who saves more than 60% of his income by focusing on cutting back on "the big three" expenses: housing, transportation and food.

"If you're renting, ask yourself whether stainless steel appliances will actually improve your life in any meaningful way," says the Minneapolis-based millennial, who goes by the pen name Sean. "If you're buying, take a long hard look at how much space you really need, and whether a mega huge yard with its mega huge maintenance is really something you want in your life."

It's important to be open-minded in general. If your dream neighborhood is going to break your budget, for example, consider other areas. The biggest mistake first-time home buyers make is not keeping an open mind, CPA Cathy Derus tells CNBC Make It.

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The No. 1 reason millennials are struggling to save for retirementand it's not debt - CNBC