A report says Yazid cursed 'Ubeidullah ibn Ziyad when he was informed of his crime, other than this I have no idea if he made Qasas or not. Allah however did make Qasas on both Ibn Ziyad and Yazid and the rest of the killers, Ibn Ziad was killed and decapitated in a war by Ibrahim bin al-Ashtar who sent his head to al-Mukhtar in 67 Hijri on the tenth of Muharram, a snake started playing with his fallen head, al-Mukhtar then sent his head to 'Abdullah ibn al-Zubair (raa) who later sent it to 'Ali bin al-Husein (raa). As for Yazid who was hanging on to his position as Caliph, he remained for four years and the people (Sahaba and Tabi'een) kept rebelling against him especially in Madinah so he wasn't even even able to rule in these short four years.