"I played horrendous. I played junior tennis or even worse. I was a little nervous because I hadn't won a match on clay all year," Williams, who will next face Spain's Virginia Ruano Pascual, told reporters.
"I was just desperate for a win and it pretty much showed in my game."
At 3-0 down in the second set, Williams bombarded Zakopalova with a series of winners to move 5-3 up after pocketing 10 points in a row but it was not enough to crush the world number 100's morale.
Zakopalova proved to be a stubborn opponent as she saved five match points in the ninth game and frustrated the American further by stretching the set into a tiebreak.
The American staved off three set points but was helpless on the fourth, failing to return a flat forehand that took a bizarre path towards her chest. That gave the Czech the tiebreak 7-5.
"I just hit the wrong shots, and then she went for broke on a few shots. I probably should have closed it out but I just didn't, and I couldn't, and I didn't want it to beat me down," Williams said.
Zakopalova, who beat Williams at the Andalucia Tennis Championships last month, kept up the momentum in the third set by breaking early before the American clawed back, winning four games in a row on a cold and blustery Suzanne Lenglen Court.
Just when it looked that Zakopalova's day in the spotlight was over, she saved three more match points at 5-2 down and then broke back in the next game.
She finally bowed out on Williams's ninth match point, allowing the Australian Open champion to clinch her first win on clay this season in two hours 25 minutes.
"I feel very disappointed. She's Serena. She's one of the biggest players here, so bad luck for the draw," said Zakopalova.
