Halep seemed to have things under control when she won the first set 7-5, but Cepelova bounced back to take a 5-3 lead in the second before clinching the set 6-4. The 22-year-old then went 4-1 up in the deciding set before upsetting the 2014 semi-finalist.
"To be honest, I have no reaction because, like I said at my first press conference on the weekend, I had no expectations for this tournament. And now here I am," she told reporters. "I knew that it would be a difficult tournament for me, but yeah, I didn't expect to lose in the first round.
"But she played good tennis today. She was fighting until the end, and she was playing aggressively when she could."
Halep was extremely disappointed to have faltered in her second consecutive grand slam as she was knocked out in the second round of the French Open when she lost 5-7, 1-6 to Mirjana Lucic-Baroni.
"Life is not always good, but I have enough power to go ahead and just think about what I have to do to do better, and just get the good feeling back on court during my matches. I just have to work hard," she said.
Despite conceding that she was low on confidence and feeling the pressure, Halep did not expect to be leaving the All England Club so soon.
"I had a few losses before coming here," she added. "My confidence wasn't too high. And during matches it's difficult because you feel the pressure, and if you aren't handling it very well, you might lose. I knew it would be difficult, but just not like today, to be honest."