Well, she didn’t “lose the election”. McGovern lost 1972.
It’s a bit of a stretch to say that she ran. She was one of the early people nominated who might have run, who had some support, but that support went away quickly. I think it’s a safe bet that many Americans never even noticed.
She was frozen out, just like Bernie Sanders and countless others who most folks have forgotten. She’s more important and more memorable than most, but a better term might be “made a bid for the presidency”.