"Votes will come and they will go, they do not trouble me," he said.
"Where we will always stand and the Australian people can always trust us to do is to have the metal to ensure the integrity of our border protection framework."
The government slammed the “shameful” move by Labor to pass the bill in the face of legal advice that the changes breached the constitution, which in turn led to warnings that the Coalition’s ability to hold power was at risk.
Mr Morrison warned the changes claimed to be humanitarian but would encourage people smugglers and risk more deaths at sea from asylum seeker boats.
The government is preparing to ramp up its attack on Labor by announcing "contingency measures" to discourage boat arrivals, with one option being the reopening of the detention centre on Christmas Island.
Mr Shorten dismissed the government claims and declared Labor would uphold national security but still treat people humanely.
"The government tells us that this bill is a constitutional crisis. The fact of the matter is this bill is about providing treatment to sick people," he told Parliament.
"We can have strong borders while still fulfilling our duty of care to the people in our care.
"This bill and our amendments are about Australia's character. It's about how we treat sick people in our care."
The final vote, shortly after 6pm on Thursday, delivered a stunning victory for Labor, the Greens and crossbench MPs to enforce new rules to give doctors more say over the transfer of refugees from Manus Island and Nauru for treatment in Australia.
The bill will go to a vote in the Senate on Wednesday, where the government does not appear to have the numbers to stop the new scheme becoming law.
Labor made a strategic move to avoid turning the bill into a test of confidence in the government, withdrawing part of the medical transfer scheme that required funding to pay for medical experts to review transfers.
The move cut short a furious debate over whether the vote in the lower house could be seen as a vote on a money bill and was therefore a vote of no confidence in the government itself.
Constitutional expert Anne Twomey, a professor of law at the University of Sydney, said the Labor decision to cut the cost of the medical panel changed the implications of the loss in Parliament.
"Now that it is no longer a money bill, and given that the government did not declare it to be an issue of confidence, the government can continue governing," she said.
"If the lower house has really lost confidence in the government, it could always move a no confidence motion, but so far it has not done so."
Professor Twomey said one parallel with the government's loss in the House was the fall of the Fadden government in 1941, when the budget was amended to reduce it by the nominal sum of one pound.
Another parallel was the fall of Prime Minister Stanley Bruce in 1929, when he went to an election after introducing an industrial relations bill and lost a key vote by 35 to 34.
Mr Shorten proved the government’s vulnerability by gaining support from five independent and one Greens MP to gain 75 votes on the floor of the House of Representatives to pass the new rules for refugee medical transfers.
In a surprise legal twist just hours before the vote, the government cited legal advice from the Solicitor-General to argue the bill would incur additional expenses by creating a panel of medical experts to rule on refugee transfers.
This launched an argument over section 53 of the constitution, which states the Senate “may not amend any proposed law so as to increase any proposed charge or burden on the people”, and led Labor to remove the cost of the medical panel to side-step the threat.
Section 53 is "non-justiciable" and therefore a court will not decide if a law is valid, meaning the government cannot challenge the medical transfer bill in the High Court.
Labor had of its 69 members as well as support from Greens MP Adam Bandt and independents Julia Banks, Cathy McGowan, Kerryn Phelps, Rebekha Sharkie and Andrew Wilkie.
"I know how much the people who are sick on Manus Island and Nauru are suffering and Parliament is saying enough is enough,"Dr Phelps said after the vote.
This bloc of 75 was enough to pass the bill over the 73 government votes and another vote from Queensland independent Bob Katter.
Mr Shorten secured the votes after giving ground on his initial proposal to the crossbench.
In the form passed by the lower house, the bill says the Immigration Minister must make decisions on each transfer within 72 hours unless the refugees should be rejected on security grounds.
The security grounds have also been clarified. In the first version of its position, Labor suggested the minister could reject transfers if the refugee had a “substantial criminal record” under a provision of the Migration Act that covers any crimes subject to prison terms of more than one year.
The later version of the Labor proposal applies the same section of the Migration Act but adds the condition that the minister must “reasonably believe the person would expose the Australian community to a serious risk of criminal conduct”.
This change is intended to protect refugees who need medical help but might have been convicted of minor offences or perhaps crimes of freedom of expression in their home countries.
Home Affairs Minister Peter Dutton and Immigration Minister David Coleman began work on contingency plans on Tuesday night in a meeting with Home Affairs Secretary Mike Pezzullo and Australian Border Force commissioner Michael Outram.