Mr Flello said that banning the sale of the animals in pet shops, garden centres and "pet supermarkets" was the easiest way to have an immediate impact on the problem.
And he urged greater clarity from the government on the powers local councils have to ban the sale of certain animals, which could potentially include puppies and kittens.
Mr Flello said: "We consider ourselves to be a nation of animal lovers where a dog is a man's best friend, a pet cat, a pet dog is part of the family. But every day puppies and kittens are bought from pet shops or garden centres that become ill. All too frequently they die as a result of the supply chain from irresponsible breeder to pet shop.
"Quite frankly I can't think a nation of animal lovers would allow this to continue. Are we at risk of becoming a nation with disposable pets?"
Mr Flello said there needed to be better public information to encourage people to only buy puppies and kittens when their mother was present.
Labour's shadow environment minister Angela Smith warned that irresponsible breeding of cats and dogs was "only the tip of the iceberg", highlighting welfare concerns about the "growing" trade in online sales.
Conservative minister George Eustice, concluded the debate saying a new voluntary code of conduct for pet sales in operation since the start of the year has resulted in 100,000 adverts from backstreet breeders being removed from the internet.
In addition, he said, puppies would not be allowed to be legally imported into Britain unless they were at least 15 weeks old, under EU rules.
He said pet shops were licensed and regulated under the 1951 Pets and Animals Act - but there was "much that can be done" to strengthen the regulations to improve animal welfare.
He promised that further guidance would be issued to local authorities to provide clarity on enforcement of rules.