The supermarket said the change will see 55% less plastic used, after some customers said it turned the mince to mush and was hard to cook with.
Campaign group A Plastic Planet said the vacuum packs will not go in most household recycling collections.
Sainsbury's said they could be recycled at stores and customers had to get used to the new look and cook differently.
The supermarket announced that it was "the first retailer to vacuum pack all mince, saving 450 tonnes of plastic each year". It is part of its goal to halve its use of plastic packaging of own brand products by 2025.
But Sian Sutherland, co-founder of A Plastic Planet, said: "While there will be a saving in the weight of plastic used, switching to flexible plastics over rigid ones is no more green than changing from a petrol to a diesel vehicle."
She said soft or flexible plastics were "almost impossible to recycle, especially where they are food-contaminated".
"The old, rigid plastic packaging would at least have gone into recycling, however limited the UK's systems are," she added. "The new vacuum packs will instead be thrown into general waste and end up in incineration."
Sainsbury's head of fresh food, Richard Crampton, told the BBC the UK was behind Europe and the rest of the world on its use and recyclability of flexible plastics. "So it's true you can't pick it up at the kerb yet," he said.
He said they had "exactly the same issue" with the film that covered the hard plastic trays the mince used to be packaged in.
"It's the same problem but now there's a lot less plastic," Mr Crampton said.
"Customers can't impact the packaging that we produce," he said, but added that Sainsbury's took its responsibility for sustainable packaging "super seriously".
"It's a moral responsibility as well as corporate responsibility - it's the right thing to do."
Environmental campaign group Wrap said plastic bags and wrapping could be recycled at more than 6,000 places across the UK. It has a recycling locator to find your nearest one.
Some shoppers had posted their dislike of the vac packed mince on social media, and reviews on the Sainsbury's website.
One said the meat now resembled "a rectangle of mushed off-cuts" and another "someone's kidney".
Mr Crampton said: "It's exactly the same mince... but more compressed... so we do need customers to cook it slightly differently.
"It's as straightforward as it just needs more agitation with a wooden spoon to break the product up," he said. The new vac packs have cooking instructions on them.
Mr Crampton said Sainsbury's had tested the move with chefs and customers and "didn't get any negative feedback at all" so felt confident to roll it out across all stores.
He said the number of complaints they had received were "fractions of less than a per cent" and sales and market share had not changed.
Asked if Sainsbury's would consider switching back to the old packaging, he said: "We always listen to customers but at the moment there's no overwhelming data to tell us to not do this."
He said vac packed meat was common in the EU and US as well as recipe boxes in the UK, and he would not be surprised if other supermarkets followed suit.