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The issue of Clinton's health has dogged her on the campaign trail, and it came into focus when she left a 9/11 ceremony early and lost her balance outside her van in New York City on Sunday.
Clinton previously attributed a cough she had to allergies, but she was diagnosed Friday with pneumonia, her doctor said.
She was placed on antibiotics.
"I'm feeling so much better, and obviously I should have gotten some rest sooner," she told CNN's Anderson Cooper by phone Monday.
"I just thought I could keep going forward and power through it, and obviously that didn't work out so well."
Clinton said that after she got into the air-conditioned van and got some water, she felt better. But she denied that she passed out.
"No, I didn't. I felt dizzy, and I did lose my balance for a minute, but once I got in, once I could sit down, once I could cool off, once I had some water, I immediately started feeling better," she told CNN.
She said she thought it was allergies, but when her cough didn't go away, she was checked by her doctor.
"Obviously, I was supposed to rest five days," she said. "That's what they told me on Friday, and I didn't follow that very wise advice. So I just want to get this over and done with and get back on the trail as soon as possible."