Krishna was not responsible for the death of the Kauravas.
Why does Krishna accept Gandhari's curse?
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There are several verses in Mahabharata which are explaining the reasons why Shree Krishna accepted Gandharis curse. Lets see them.
After the kurukshetra war was over and the the ladies of race of kuru visited battlefield and there they saw the dead bodies of all their loved ones. They started moaning after that in great grief. Gandhari at that time burning with grief complained and expressed her objections towards Shree Krishna of not stopping this great war and massacre even he was capable of doing so. She accused Shree Krisha being indifferent to Kauravas and Pandavas. As mentioned in Mahabharata - Stri Parva- Chapter 25.
O Janardana, why wert thou indifferent to them? Thou wert competent to prevent the slaughter, for thou hast a large number of followers and a vast force. Thou hadst eloquence, and thou hadst the power (for bringing about peace). Since deliberately, O slayer of Madhu, thou wert indifferent to this universal carnage, therefore, O mighty-armed one, thou shouldst reap the fruit of this act. By the little merit I have acquired through waiting dutifully on my husband, by that merit so difficult to attain, I shall curse thee, O wielder of the discus and the mace! Since thou wert indifferent to the Kurus and the Pandavas whilst they slew each other, therefore, O Govinda, thou shalt be the slayer of thy own kinsmen! In the thirty-sixth year from this, O slayer of Madhu, thou shalt, after causing the slaughter of thy kinsmen and friends and sons, perish by disgusting means in the wilderness. The ladies of thy race, deprived of sons, kinsmen, and friends, shall weep and cry even as these ladies of the Bharata race!
जानेsमेतदप्येवं चीर्ण चरसि क्षत्रिये |
दैवादेव विनश्यन्ति वृष्णयो नात्र संशय : ||48 ||
There is none in the world, save myself, that is capable of exterminating the Vrishnis. I know this well. I am endeavouring to bring it about. In uttering this curse, O thou of excellent vows, thou hast aided me in the accomplishment of that task. The Vrishnis are incapable of being slain by others, be they human beings or gods or Danavas. The Yadavas, therefore shall fall by one another’s hand.’
Shree Krishna was well capable of diverting this curse , but he did not do so , one of the reason is to respect Gandhari's curse and words and to make them true , which she uttered in anger. He incited the curse by asking Yadavas to make pilgrimage. This is mentioned in Mahabharata - Mausala Parva - Chapter 2
इत्युक्त्वा वासुदेवस्तु चिकीर्षु: सत्यमेव तत् ||
आज्ञापयामास तदा तिर्थयात्रामरिंदम : ||23 ||
Vasudeva, having said so, endeavoured to bring about those occurrences which would make Gandhari’s words true.. That chastiser of foes commanded the Vrishnis to make a pilgrimage to some sacred water.
So Shree Krishna accepted Gandharis curse because - :