Despite the embarrassing defeat, 75-74, Mr Morrison said he had no concerns crossbench MPs would now act to bring down the Government in a motion of no confidence.
He said Australia's border protection regime could not be adjusted without serious consequences.
The doctors were due to be paid under the original proposal - but Labor's late change to exclude remuneration means the bill can not be rejected on constitutional grounds.
Morrison's own approval rating gained 2 points, however, against Labor leader Bill Shorten, climbing to 44 percent from 35 percent.
The Senate will look at some legislation dealing with recommendations from the royal commission, while the lower house will consider laws making it compulsory for candidates to reveal if they are eligible to sit in parliament.
Following the defeat, Prime Minister Scott Morrison attacked the "damaging impact of what Labor has done tonight".
"He (Bill Shorten) can not be trusted on our borders and Australia can not trust Bill Shorten on border protection", he said.
"The Labor party and Liberal-National party are not on the same page when it comes to border protection".
'I believe we can keep our borders secure, we can uphold national security, but still treat people humanely'.
The latest polls show Labor is heading for a solid victory at the next federal election, but Mr Morrison told a joint coalition party room meeting they had a chance.
The fiery attack on Mr Shorten, following an earlier exchange on the chamber floor.
When the sitting government last lost a vote on substantive legislation in 1929, then prime minister Stanley Bruce immediately called an election, and lost it. "This is now on your head, Leader of the Opposition".
The government is looking to block a bid, led by an independent, to allow asylum seekers in offshore camps to come to Australia for medical treatment, saying migrants could exploit it as a way into the country.
Scott Morrison urged parliament to reject the medical transfers bill.
"Let Your compassion come to me that I may live, for Your law is my delight", the prime minister read at the annual church service to mark parliament's return.
The amendments agreed between Labor and the crossbench widen the discretion of the home affairs minister to stop medical transfers if asylum seekers pose a security risk or have serious criminal records.
A medical panel of two doctors would assess requests for medical transfers of people now on Manus Island and Nauru, but not new arrivals.
Solicitor-general Stephen Donaghue QC argued the amendments could breach the constitution because of the payment issue, but ultimately it was up to parliament to decide if they did or not.