The 27-year-old, who received an emotional welcome from other players in Paris after her first round at Roland Garros, said she's hoping things will return to normal on the grass.
"The Slams are what's driving me more than the number one ranking".
"Last year I performed well in the Slams with finals in Australia and France, a win at Wimbledon and the quarter-finals at the US Open".
Home favorite Jo-Wilfried Tsonga also exited the tournament, unable to turn around a first-round match against Roland Garros debutant Renzo Olivo that had been suspended on Tuesday due to darkness.
In a match featuring 12 breaks of serve, Svitolina hit 13 winners and limited her mistakes to eight unforced errors in the final set.
Andy Murray later easily won his first round match beating Russia's Andrey Kuznetsov 6-4 4-6 6-2 6-0.
The big-serving Croatian, who had 11 aces, broke Kravchuck's serve at love to end the Russian's Roland Garros debut. Dominic Thiem, the sixth seed, is another popular pick by experts and he breezed through Simone Bolelli, 7-5, 6-1, 6-3, on Wednesday.
In match between two emerging talents, Daria Kasatkina came through.
Marketa Vondrousova's first round win over Amandine Hesse extended her winning streak to nine, and was her 51st victory of 2017.
Konta, who is now the world number eight, then failed to convert any of her four break points at 5-4 before netting a return to hand Hsieh the match.
Tsonga had never lost to a player ranked as low as No. 91 at a Grand Slam.
Klizan was involved in a controversy in his previous match after Laurent Lokoli accused him of faking injuries during their match, and refused to shake his hand.
Petra Kvitova lost in the second round of Roland Garros but left Paris with two more matches under her belt than many expected, as well as one of the moments of the tournament already. Pliskova faces Ekaterina Alexandrova, Halep takes on Tatjana Maria, and Svitolina meets Tsvetana Pironkova.