The masses interpret victory and defeat in the language of general warfare. Going by this, they deem Yazid as the victor, while Imam Husain (a.s.) is deemed the vanquished one.
However, this was not general warfare, nor a battle between two princes as is commonly stated to defend Yazid.
This was a battle between the Proof of Allah and his challenger, a conflict between truth and falsehood. Hence the usual interpretations of victor and vanquished do not hold true over here. The mere declaration of Yazid’s caliphate was falsehood, leave alone challenging Imam Husain (a.s.) in battlefield.
An interesting incident sheds light on who was the real victor in Karbala.
Imam Jafar Sadiq (a.s.) informs –
When Imam Ali Ibn Husain (a.s.) entered (Medina) after Imam Husain Ibn Ali (a.s.) had been killed, Ibrahim Ibn Talhah received him and asked – O Ali Ibn Husain (a.s.) – who was the victor (in Karbala)?
Imam (a.s.), while he was in the litter, with his head covered, replied him – If you wish to know who is the victor, whenever it is time to pray, then recite the azaan and iqamah.
Al-Amaali of Shaikh Tusi (r.a.) p. 677, 884
Behaar al-Anwaar v 45 p 177
Yazid was out to erase all signs of Islam beginning with Imam Husain (a.s.).
Although he evidently succeeded in his mission by massacring Imam Husain, religion of Islam continued to shine as bright as ever.
The invitation to Tauheed and Prophethood continued to reverberate in the daily azaan and iqamah. This marked a victory for Imam Husain (a.s.) who set out exactly with the purpose of securing the religion of his grandfather (s.a.w.a.) from the clutches of tyranny and oppression.