The bench comprising Chief Justice J S Khehar and Justice D Y Chandrachud asked the lawyer, who mentioned the issue before it, to approach the Allahabad High Court with his grievances.
The lawyer has also sought an SIT probe into the deaths of children at the Baba Raghav Das Medical College (BRD) Medical College in Gorakhpur.
The court observed that the authorities were handling the situation and the grievances, if any, have to be raised before the high court concerned.
Over 60 children have reportedly died at BRD Medical College Hospital since August 7, many for want of oxygen whose supply was disrupted after bills were not paid to the vendor.
At least 30 children were reported dead in the last two days alone. Many of the victims were infants who perished in the neo-natal intensive care unit.Police had said no case has been registered so far in the absence of a formal complaint.
The state government had on August 12 ordered an official inquiry by the chief secretary and suspended the principal of the Medical College Hospital Rajiv Mishra.