Charqual McMath, 28, was behind the wheel when she swerved and lost control of her SUV on the President George Bush Turnpike Saturday night.
But her sister Torneki McMath, 19, her daughter, Tyreana McMath, 12 and her niece Myaa Moore, 13, were killed.
"I just wish it would've happened another way," McMath said. "I just hate that it happened to my family like that. I wish there was something I could have done."
McMath was headed east on the turnpike near the U.S. Highway 75 overpass in Richardson when traffic began to slow down.
"We were on the George Bush Turnpike going up, and next thing you know cars are slowing down, so I swerved to avoid the cars," McMath said. "I didn't even know we went off a bridge until we fell. I was like, 'How did we get down here?' I was panicking. I was just trying to get everyone out of the car."
The investigation into the crash is ongoing. Police said drugs or alcohol don't appear to be a factor.
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Michael Rey, spokesman for the North Texas Tollway Authority, said, in a statement to NBC 5: "DPS is still investigating the crash. NTTA will review DPS's report when it is complete. All NTTA roadways, including this one, are designed and constructed to meet all state and federal safety regulations."