Paolini's dream of an Olympic medal after disputing the finals in the French Open and Wimbledon this year were still alive, however, as she continues in doubles alongside Sara Errani later in the day at Roland Garros.
"She was definitely more consistent than me today, more focused as well and I'm a bit disappointed with the match, but it's tennis it can it can happen, so now I have to focus on doubles," she said.
After leading 5-3 on the red clay in the first set, the Italian had a dip in form, having a hard time returning some of Schmiedlova's long groundstrokes in losing the next four games and the set.
Paolini won the second set easily, but a fresh load of unforced errors - 52 against 32 for the whole match - and a lack of focus caused her to lose the third despite having served for the match at 5-4.
"Unfortunately, mentally I didn't feel 100% clear and I think the emblem is the 5-4 serve," she said.
"There was definitely a bit of nervousness, I really wanted to do well and I think this made me put a little more tension."
In the doubles second round, Paolini and Errani will face France's Caroline Garcia and Diane Parry, their supporters and the heat wave hitting Paris on Tuesday.
Meanwhile, Schmiedlova cheered what she said was one of the biggest wins of her career.
"It was very tough, very hot. I didn't have a lot of power at the end, but I made some brave decisions and it worked out," she said. "I had nothing to lose."