Following a period of ill-health, Maradona died at the age of 60 after suffering a cardiac arrest in Buenos Aires last Wednesday.
Luque recently treated Maradona for a blood clot in his brain but discharged him a fortnight ago following a successful surgery.
Luque has not been charged but is under investigation for ‘involuntary manslaughter’ in Maradona’s death.
"We were all gathered to see the best for Diego: the doctors, myself, his family. Nothing could be done without his will," Dr Luque told reporters on Sunday.
"We sought to put together a containment scheme for the issue of the pills he was taking and to control alcohol consumption.
"There were no medical criteria [to keep Maradona in hospital]. We could have taken him to a rehabilitation centre, but we needed Diego's okay. It was his decision.
"Here there are no decisions, there are medical criteria. When you operate on a patient, the discharge criteria depend on the patient. There wasn't a doctor error.
"He had a heart problem that can happen in a patient like him. Everything possible was done to reduce that chance, but you cannot block the possibility.
"I had the full endorsement of the Argentine Society of Neurosurgery that Diego needed the surgery. Six doctors evaluated him. Death had nothing to do with [the surgery]."
Dr Luque added: "He was discharged after surgery. The ideal thing would have been for him to undergo rehabilitation, but he did not want to. We managed to get a nurse to accompany him, but he had the medical discharge.
"We tried to keep him in the clinic, but it is not a rehab centre. I extended the hospitalisation as long as I could. I am at the disposal of the justice department. With Diego, I did the best I could. I am proud of what I did. I have nothing to hide."
The former Barcelona, Sevilla and Napoli star was laid to rest on Thursday as thousands of people trooped to his funeral to pay their last respects to a man many consider as the greatest footballer of all-time.
