After the BBC failed to make a bid, the ECB announced a £300m four-year deal starting in 2010 which allows Sky to show all live domestic and international cricket.
Giles Clarke, the ECB chairman, said that the board had been prepared to listen to all offers, no matter how small, for any part of the package. He called for a debate on the whole issue of public sector sports broadcasting.
He said: "All these people interested in cricket buy TV licences and surely they should have a right to expect the public sector braodcasters to mount bids for the nation's summer sport?"
Referring to the BBC's recent £40m-a-year deal to show live Formula One, he added: "After all, just how many people play Formula One?
"There are 19m cricket fans, 2.5m men and boys and 900,000 women and girls who play the game. Surely they have a right to expect public service broadcasters to mount bids for the nation's summer sport?"
But the BBC described the criticism as "astonishing" and claimed that the price of cricket is now beyond terrestrial broadcasters.
Until ten years ago, Test matches at Lord's were on the list of events protected by law to be offered to free-to-air organisations at a rate described as "fair and reasonable".
The highlight of the package announced yesterday will be the 2013 Ashes and also includes 26 Test matches in all as well as 46 one-day internationals
A spokesman for the BBC said: "We are astonished by these comments from the ECB. We have always said that any bid for live Test cricket would be subject to value for money and being able to fit into the scheduling. In our view neither of these criteria were met.
"We have consistently argued that not having cricket as a listed event puts it out of the reach of all terrestrial broadcasters. It is absurd to blame the BBC for this outcome."