"Today I am happy that not only us, but the Supreme Court also sees it and understands that what has happened was wrong," Abdullah told reporters on the sidelines of a book release function held here.
The CJI's remarks came against the backdrop of the family of Parliament attack convict Afzal Guru not being informed about his hanging in due time.
Abdullah said his party has time and again highlighted that Guru's family was not given a chance to meet him.
The minister, however, said discussing the issue over and over again would "only lead to pain".
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"Whatever has happened has happened, if we will time and again beat around it, we won't be able to heal the hearts of people. It will only lead to more pain.
"The time has come that we should make attempts to correct the mistake and ensure that no such mistake is committed in the future," Abdullah said.
The communication regarding the rejection of Guru's mercy plea and his subsequent execution had reached his relatives two days after he was hanged on February 9.
On having any prior intimation about Guru's execution, he said, "Central government has got its own powers and they used their powers without saying anything to the state government. I am also a member of the government, I was not informed. I came to know like everybody else".