Which? said Tesco, which has a 27% share of Britain's grocery market, should be working harder to make food more affordable for consumers while Unite accused Tesco of "rampant profiteering".
"How can it be that at a time when millions are struggling to feed their families Britain’s biggest supermarket is profiteering as never before," Unite general secretary Sharon Graham said.
She was also critical of Tesco's announcement it would buy back a further £750 million (€849 million) of shares this year.
'Good Job For Consumers'
However, Tesco Chief Executive Ken Murphy said the supermarket group was doing a good job for consumers, with its inflation "dramatically below" the headline figure of over 17% reported by market researcher Kantar. He did not give a figure.
"The key point I'd make ... is that our profits fell by 7% this year and that is despite the fact that we achieved a record level of cost savings," he told reporters.
"That for me is a very material proof point that we worked very hard for both customers and for colleagues this last financial year."
Murphy said Tesco, which has a profit margin of about 4%, needed to be able to invest in all parts of the business and for all stakeholders - customers, its 330,000 employees, suppliers and shareholders.
"Shareholders have been very supportive, despite a meaningful increase in our top-line sales number, they have seen a significant fall in the profitability of the business," he said.
"They would argue and we would argue very strenuously that we got the balance right this year in making sure that we were very competitive."
Murphy added he was "very comfortable" with the share buy back as it was balanced with what the group was doing for other stakeholders.