"Misguided altruism" was "leading much of Europe into catastrophic error," Mr Abbott said during a speech in London.
As PM, Mr Abbott carried out the controversial policy of turning away migrant boats, sending them elsewhere.
Retired Bishop Pat Power said he was "ashamed" by the comments, the Sydney Morning Herald reported.
Bishop Power in particular objected to Mr Abbott's suggestion that a "wholesome instinct" to follow the Christian tenet of "love thy neighbour" had led Europe to feel obliged to accept more people fleeing conflict in the Middle East that they could cope with.
"People will make their own judgements but that's completely at odds with what's at the heart of Christianity," Bishop Power told the newspaper. "I'm certainly offended."
Father Frank Brennan, professor of law at Australian Catholic University, told 3aw Mr Abbott's comments were "outrageous".
He said German Chancellor Angela Merkel - who has won praise and criticism for her welcoming stance to migrants - should ignore the speech.
"I don't think she's helped in the least by an ex-prime minister who has been dumped at the other end of the world turning up and saying 'it's about time you got your naval vessels to start returning people to places like Libya'."
Australian Foreign Minister Julie Bishop gave her backing to Mr Abbott, saying her country had a "very appropriate and strong and tough border regime".
Australian asylum: Why is it controversial?
Mr Abbott made the comments at the annual Margaret Thatcher lecture to an audience of governing Conservative party members and ministers, as Europe faces an unprecedented surge in the number of people trying to reach its shores.
The former Australian leader, who is Catholic, said his country was the only one to have successfully defeated people-smuggling.
Nigel Farage, leader of Britain's right-wing Ukip party, tweeted that the speech was "absolutely bang-on".
But others have given it a hostile reaction - political blogger Guido Fawkes said members of British Conservative party present had "winced" while listening on.
Social media users mocked the Biblical references in the speech using the #TheToneCommandments hashtag.
Prominent Australian Catholics have attacked a speech by ousted PM Tony Abbott in which he urged Europe to take a hard line on migrants.