The Bradford-based firm said customers have become quite "cautious and careful" amid the uncertainty over Brexit.
Morrisons' chief executive David Potts told The Yorkshire Post: "If customers are feeling the pinch, we have to be there for them, offering great value for money.
"It feels like a year to be there for customers - to be a beacon of trust for customers."
He was speaking as Morrisons announced a rise in sales over the festive period thanks to its decision to keep prices low.
The grocer said the price of its basket of 100 key Christmas items was the same as last year, leading to a modest 0.6 per cent increase in like-for-like retail sales. The real growth came from wholesale which saw a 3.0 per cent increase in like-for-like sales thanks to Morrisons' tie-ups with the likes of McColl's and Amazon.
This led to like-for-like sales growth of 3.6 per cent in the nine weeks to January 6, its fourth consecutive Christmas of like-for-like sales growth.
Morrisons has shied away from mentioning Brexit as a factor in the past, but Mr Potts said there was a change in consumer behaviour during the run up to Christmas.
"We spend quite a bit of time listening to customers," said Mr Potts.
"Customers were possibly feeling the effect of quite a spend up surge in the summer with the heatwave and football success.
"The uncertainty over Brexit - it's possible that has started to become more personal as the season progressed. Customers are quite cautious and careful.
"It was a tough October, November felt like October, but it got better towards the end. Towards the end of the period, customers decided to go for it a bit more - in the last four or five days."
He said that both affluent and price sensitive customers were keeping a check on their spending.
"That's why we were keen to keep the price of 100 items the same price as the previous year. That definitely resonated. It's the things that people buy traditionally."
Mr Potts said that this is the second year that festive shop prices have been maintained, which effectively means the customers paid the same as they did in 2016.
When asked about the impact a no-deal Brexit could have on food imports, he said Morrisons is working closely with its suppliers and freight partners.
"Two thirds of what we sell is British, " he said.
"We've got 18 factories in Britain. Whilst we are not immune, we are a bit different."
Thomas Brereton, retail analyst at GlobalData, said: "As the first of the big four supermarkets to release Christmas results, Morrisons announced marginally better than expected like-for-like sales over the period, beating analyst expectations of near-flat growth.
"It is tipped to be the least vulnerable of the big four in the event of a challenging Brexit, given its vertically integrated supply model (about 25 per cent of own-label product is produced internally) and growing wholesaler opportunities providing security through diversification.
"But with pressure mounting from both the discounters and its big four rivals, it will need to ensure both organic in-store success and development of its immature online business in order to vie effectively for market share."
Morrisons reported strong sales of vegetarian and vegan options with a three-fold increase in the sale of nut roasts to 20,000. It also saw strong demand for vegan "veggies in blankets" with sales of 55,000 packs, up from zero the year before.
"Wonky" vegetable sales doubled and the group sold a million of them over the Christmas fortnight.
It sold 8 million bags of vegetables on sale for three for £1 during the Christmas week. This was rise of 10 per cent and led to the sale of 10,000 tonnes of vegetables, which Mr Potts described as "a stand out performance".
On Monday, Morrisons cut the price of 935 products by an average of 20 per cent in a bid to attract budget-conscious, post-Christmas shoppers.