Professor Goodall took his own life on Thursday at a clinic near Basel, to the strains of Beethoven's final symphony and surrounded by family.
Dr Goodall ate his favourite dinner of fish and chips, followed by cheesecake, for his last meal on Wednesday evening, Dr Nitschke said.
Swiss doctors are divided on the issue of assisted suicide.
"It would have been much more convenient for everyone if I had been able to, but unfortunately it failed", he said of the suicide attempt.
He told reporters: "One should be free to choose the death, when death is at an appropriate time".
He was not terminally ill but said he had grown exhausted of living with deteriorating health.
Though Goodall was not terminally ill, he had seen his eyesight and mobility deteriorate considerably in recent years and said that his life stopped being enjoyable "five or 10 years ago".
That law doesn't come into effect until mid-2019 and would not benefit Goodall because he is not terminally ill or suffering from an incurable disease.
David Goodall ends his life at 104 with a final powerful statement on euthanasia
However, a handful of nations - including Belgium, Luxembourg and the Netherlands - have legalised one or both of the practices, according to the nonprofit group ProCon.org.
Goodall asked not to have a funeral or remembrance service.
"David Goodall is exactly the sort of member that Exit is made of and is proud of", Nitschke said.
His supporters applauded his decision to take charge of his fate after declaring his life was no longer worth living.
An honorary research associate at Perth's Edith Cowan University, Mr Goodall has produced dozens of research papers and until recently continued to review and edit for different ecology journals.
"David Goodall would have never satisfied the criteria needed", he said.
Speaking shortly before his death, Goodall expressed joy that he no longer wishes to continue with life.
Several family members were with Goodall until his death, which was preceded by formal paperwork that visibly frustrated Goodall, who said "What are we waiting for?"
"The process of dying can be rather unpleasant, but it need not be", he said. 'I'm happy to have the chance tomorrow to end it'.
"I certainly hope my story will increase the pressure for people to have more a liberal view on the subject (of voluntary euthanasia)", he said.