Australian Grand Prix Corporation (AGPC) Chairman Ron Walker had already expressed his misgivings to Ecclestone, the organiser's CEO Andrew Westacott told Fairfax radio on Monday.
Westacott said the quieter cars had taken something away from the F1 spectacle for fans at the race.
"One aspect of it was just a little bit duller than it's ever been before and that's part of the mix and the chemistry that they're going to have to get right," Westacott told Fairfax Radio on Monday.
"Ron spoke to (Ecclestone) after the race and said the fans don't like it in the venue.
"We pay for a product, we've got contracts in place, we are looking at those very, very seriously because we reckon there has probably been some breaches."
The season-opening Grand Prix in Melbourne raised the curtain on F1's technological revolution, which includes new turbocharged hybrid engines.
Some pundits have bemoaned the quieter cars, saying they preferred the more robust noise of the previous V8 engines.
Team principals of the major F1 outfits shrugged off the change at Albert Park, saying fans would get used to it.
Formula One management was unable to provide immediate comment. The Singapore office of private equity group CVC Capital, the largest shareholder in Formula One, declined to comment when contacted by Reuters and referred enquiries to their London office, which was closed.
Australia's Victoria state government has yet to sign an extension to the grand Prix contract, which expires in 2015.
Walker said this week that the AGPC had hammered out a new deal to keep the race in Melbourne with F1 management but it needed to be signed off by the state government.
A Victoria government minister in charge of tourism and major events said the government wanted to keep the race and that only cost would be a consideration. She said there was "no rush" to sign, though.
Recent races have cost Victoria taxpayers more than A$50 million ($45.19 million) a year.
Germany's Nico Rosberg won the season-opener at Albert Park for Mercedes.
- Sports & Recreation