The Greeks (Spartans and allies) knew they were outnumbered and hadn't a prayer, so it was no surprise that the Persians won the Battle of Thermopylae. However, their courage provided inspiration to the Greeks, hence a victory in defeat.
Thermopylae (lit. "hot gates") was a pass the Greeks tried to defend in battle against the Persian forces led by Xerxes, in 480 B.C. Although Greece lost at Thermopylae, the following year they won battles fought against the Persians.
The Battle of Thermopylae is believed to have been fought in August 480 BC, during the Persian Wars (499 BC-449 BC).
Casualties are not known with any certainty, but may have been as high as 20,000 for the Persians and around 2,000 for the Greeks. With the defeat on land, the Greek fleet withdrew south after the Battle of Artemisium.
As the Persians advanced south, capturing Athens, the remaining Greek troops began fortifying the Isthmus of Corinth with the fleet in support.
In September, Themistocles succeeded in winning a critical naval victory at the Battle of Salamis which forced the bulk of Persian troops to withdraw back to Asia. The invasion was brought to an end the following year after the Greek victory at the Battle of Plataea.