Stosur lost in two tie-break sets to Lucie Safarova despite having her chances in both sets on Saturday and with Jarmila Gajdosova also losing to Kvitova, Australia had no wriggle room on Sunday at the Cez Arena in Ostrava.
Kvitova and Stosur were then first up on Sunday with Stosur needing to win to keep Australia alive in the first round Fed Cup match-up.
The world No. 9 made the ideal start winning the first set 6-2 in just 27 minutes after managing to convert two of her three points against the 2011 Wimbledon champion.
Stosur had a match point when leading 5-4 in the second set but Kvitova fought back to get it to a tie-break which she was able to end up winning seven points to three despite coughing up an early service mini-break.
There was a combined six breaks of serve in the second set and then Kvitova broke Stosur's service twice to lead 5-0 in the third set, but the Australian wasn’t ready to lie down and meekly concede.
Stosur got the set back on serve breaking Kvitova twice, but the Czech star broke Stosur's serve again to win the set 6-4 and secure the match, and tie, for the Czech Republic.
Stosur was actually pleased with how she performed in a tough match with Kvitova.
"I was very happy with the way that I was playing and it was just one that slipped away. I really don’t think I did much today, though, and I think Petra played a very good match," Stosur said.
"Once that second set started I thought we were both playing at a high quality and when it comes down to that it is decided by a point here and a point there.
"I really found myself behind the eight-ball at 5-0 in that third set, but I kept trying to hang in there and thought that I was still capable of winning and kept trying to play the way that I wanted to be playing. I came close in the end."
The reverse singles encounter wasn’t played between Safarova and Gajdosova with the tie decided, but the doubles did take place with Czech pair Lucie Hradecka and A Hlavackova beating Australia's Casey Dellacqua and Ashleigh Barty 6-0, 7-6 (1).
Even though Australia came into the tie big underdogs against the defending Fed Cup champions, they will be disappointed to go away with a 4-0 defeat with Stosur having her chances in both singles matches, and even Gajdosova putting up a good fight against Kvitova on Saturday.