Processed goods like jelly or gravy could be unavailable in NI at the end of the protocol grace period, according to Stormont's agriculture minister.
Edwin Poots acknowledged Northern Ireland has plenty of homegrown produce, such as beef or potatoes.
But he warned trimmings like Bisto or trifle could be missing from traditional Sunday dinners.
He also stood by his claim that action was needed to avert "a major crisis" over food supplies.
However, political opponents have accused him of scaremongering.
Mr Poots said the official minute of a meeting he held with suppliers - at which he was told of a potential problem supplying schools, hospitals and prisons - backs him up.
Speaking in the Northern Ireland Assembly on Monday he repeated his claim and accused media outlets, including the BBC, as well as other politicians, of being "disingenuous".
"That was what the minute of the meeting described. Not my minute - the official minute of the meeting.
"So the BBC and other media outlets, indeed other politicians, may seek to undermine what I said and try to create some discrepancy in terms of the veracity of it (but) the minute is there."
A soft-touch three-month period has been negotiated with the EU for regulating supermarket goods transported from the rest of the UK following the end of the transition period.
Mr Poots said these "cliff edges are where the issues become really more problematic".
"We do not need these barriers," he added.
"We need common sense, particularly from the EU.
"We need a message going out from all of our companies that we do not need barriers which are going to put costs on."
Last week, officials in Northern Ireland said they have not experienced major disruption to the supply of food to hospitals and schools due to Brexit.
Mr Poots also claimed that "rigorous implementation" of the Protocol would mean "numerous items" would be missing from supermarket shelves in Northern Ireland.
Some supermarket shelves were depleted this month as suppliers grappled with new rules surrounding sending goods from the rest of the UK to Northern Ireland.
The protocol means Northern Ireland follows the EU's rules on matters like animal product standards and creates extra paperwork on goods travelling from Great Britain.
NI 'integral' to UK internal market
Meanwhile, the economy minister said Northern Ireland remained an integral part of the UK's internal market, with equal access to the other nations.
However, Diane Dodds warned of the impact on products like steel, which could face tariffs of up to 25%.
It is deemed by the EU to be at risk of entering the single market when arriving in Northern Ireland from the rest of the UK.
Cabinet Minister Michael Gove engaged in talks with Mrs Dodds on Friday.
"I am encouraged that, following our representations, the government know that this is a huge issue for Northern Ireland and we need to see a resolution."
She envisaged a statement coming from the government in the coming days on the issue.