One customer told the BBC she has missed out on her online order, which included a turkey and trifle that was meant to arrive this afternoon.
“I booked it ages ago, when the delivery slots first came out for Christmas,” says Moira Redhead, from Northumberland.
She is unable to leave the house due to illness, and is waiting for a medication delivery today.
“I’m really stressed, I don’t know what I’m going to do,” she says.
“[Morrisons] said they couldn’t do anything… they also said their systems were down,” she adds, saying that Morrisons offered a £10 goodwill voucher.
Another customer says he missed out on about £20 of discounts.
“I added everything up as I went around the shop and it came to £70, which with all my card discounts and vouchers should have cost me nothing at the checkout,” Steve Weatherby, from Huddersfield, told BBC News.
“But it came up as £90. None of the discounts and offers around the store, like 50p off, had been applied.
“So I had to pay it as I was shopping for Christmas lunch and things we needed.”
He added: “The staff were getting upset as they weren’t aware of what was happening, and it’s not their fault.”