Mr Lamy said that it was up to Washington to make concessions over the subsidies it pays US farmers, and Brussels to offer more access for agricultural imports into the EU.
Key emerging nations such as Brazil and India should in turn cut barriers to commerce in industrial goods.
"I believe that the ministers in each of these big constituences know that as well," Mr Lamy said. "What they've tabled is not enough."
"Starting from what is on the table, the only solution is stretching in the three directions," said Mr Lamy, speaking after a gathering of trade diplomats.
With the trade talks a year behind schedule disputes among the key WTO players have proven a particular sticking point during the Doha Round of negotiations.
Mr Lamy urged governments to stop trading blows, after verbal jousting last week over the sluggish pace of talks: "This is not a time for blame or recrimination."
On Friday, gloomy WTO negotiators had said that because of persistent differences they would be unable to reach agreement on a crucial part of their talks, the mathematics for cutting tariffs and other trade barriers, by the target date of April 30.
Modalities missed
In WTO jargon, this plank of the Doha Round is known as "modalities." Mr Lamy confirmed on Monday that the deadline was out of reach.
"We need to face facts squarely: there will not be modalities on agricultural and industrial tariffs by the end of April," he said, adding that governments must try to catch up "in weeks rather than months."
He added: "Clinching the modalities is probably the key moment of this round."
Missing the April 30 target has been regarded as a setback to efforts to complete the long-delayed round, which was launched in 2001 with the aim of tearing down barriers to commerce and using trade to boost the economies of poor nations.
Mr Lamy, however, took a more positive tone: "We have missed a deadline but we have no deadlock. Negotiations have been moving foward, but clearly at a pace which is too slow to reach modalities.
"I don't think it's good news for the round, but I don't think we should cry over the missed deadline," he said.
"What we need is more determination and a clearer sense of purpose," he said.
Negotiators also face a July 31 target to set out in detail how governments would implement a formal trade treaty at the end of the round. The Doha Round was originally meant to end in 2004.
The deadlines were part of efforts to complete the round by the end of 2006, before the White House loses its special authority to negotiate trade deals.
In July 2007, US Congress is set to regain its power to pick apart any trade accord, and that has the potential to complicate future talks.
"We have to face this reality. The end of 2006 remains the overall deadline," said Mr Lamy.