The retailer posted a 3.7% drop in like-for-like sales for the first quarter to May 24 as it battled with intense competition from discount rivals amid a continuing upheaval in customers' shopping habits and a squeeze on household budgets.
It was the third quarter in a row of worsening falls and Mr Clarke, who is in his 40th year at the store after working his way up from the shop floor, warned there was no prospect of an end to the gloom any time soon.
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He said: "There hasn't been a quarter of like-for-like sales like this before that I can remember, but I've never seen a period of such intense transformation for the industry."
Tesco, like its rivals, is facing a squeeze from discounters Aldi and Lidl and latest industry figures show its market share has declined steeply.
It has responded by investing in price cuts on "the products that matter most" - and Mr Clarke said sales volumes had risen 28% in these areas, with more cuts to come. The retailer is also in the midst of a "refresh" programme to update stores.
Other changes include a cut in delivery charges while click-and-collect has been made free and a Clubcard Fuel Save offer has been extended across the country.
The chief executive said Tesco was "more competitive than we have been for many years" but warned that intensifying efforts on price and refurbishment continued to impact on like-for-like sales performance.
He said: "We expect this acceleration to continue to impact our headline performance throughout the coming quarters and for trading conditions to remain challenging for the UK grocery market as a whole."
The latest decline comes after drops of 1.4% and 2.9% in previous periods.
Mr Clarke insisted the group had expected to see like-for-like sales worsen as it sought to invest in "delivering real benefits for our loyal customers", with permanent price cuts targeted rather than short-term promotions.
"Loyalty is the prize worth having and we are putting our effort behind that," he said. "Our plan is about positioning Tesco for the future.
"I know it's going to take time for changes to stop weighing on our performance.
"We have got positive momentum in the business and we can see underlying how the strategy will return us to growth."
The chief executive refused to be drawn on when sales would start to increase again.
He said: "I see every day the improvements that are coming in the business but I am not making any promises about sales improvements in the next few quarters."
Mr Clarke pointed to a shift in shoppers away from the "one-stop shop" of out-of-town stores towards convenience outlets - where he said Tesco Express saw a quarterly improvement - and the internet.
He also pointed to years of decline in real-terms wages squeezing consumers and argued that, despite recent signs of optimism, "for the majority of customers it is not getting into their pockets".
Mr Clarke pledged that its price-cutting strategy would be better than its "big price drop" in 2011, admitting of that campaign: "We didn't execute it very well."
He said this time that "prices are down and they are staying down" and pointed to a promotional campaign to draw customers' attention to this.
The chief executive recently unveiled a second year in a row of declining profits, two years after unveiling a £1 billion turnaround plan for Tesco.
He declined to reveal whether investors continued to back his strategy, saying conversations with them remained confidential.
Mr Clarke said a reduction in "short-term, indiscriminate couponing" had accounted for much of Tesco's "underperformance relative to the grocery market" compared to the final quarter of last year.
The group "refreshed" 100 stores in the quarter and plans to revamp 200 more by the end of the first half.
Online changes saw Tesco achieve the milestone of more than 100,000 daily orders for the first time.
International sales increased by 0.5% but, after accounting for currency changes, saw a decline of 8%.
Performance in Asia started to improve despite turbulence in Thailand while like-for-like sales were positive in the Czech Republic, Hungary, Poland, and Turkey. Ireland remained "intensely competitive" but performance was also getting better.
Shares rose 1% following the update, which was not as bad as some forecasts predicting a UK like-for-like sales decline of more than 4%.
Richard Hunter, head of equities at Hargreaves Lansdown stockbrokers, said: "Investors need to ponder whether Tesco is a company showing glimpses of revival given its turnaround plan, or whether it is past its sell-by date."
Tesco has more than 3,000 UK shops employing more than 300,000 people, with annual sales of £48.2 billion at home and £70.9 billion overall.