Walker claimed Ecclestone was "horrified"by what he had heard on Sunday, to which the 83-year-old said: "I was not horrified by the noise, I was horrified by the lack of it.
"And I was sorry to be proved right with what I've said all along - these cars don't sound like racing cars.
"I've been speaking with Jean [Todt, president of the FIA] and what I've said is we need to see whether there is some way of making them sound like racing cars."
Speaking to The Daily Telegraph, Ecclestone added: "I think let's get the first few races out of the way and then maybe look to do something. We can't wait all season. It could be too late by then."
The 83-year-old had also chatted with Ferrari president Luca Di Montezemolo, who informed Ecclestone he had been bombarded with emails of complaint.
Mercedes Motorsport boss Toto Wolff, who started the campaign on a winning note with Nico Rosberg taking the chequered flag at Albert Park in Melbourne, has suggested the teams could look into the issue.
"For me personally - I would judge the new F1 era as a success. It's mind-blowing technology," enthused Wolff. "But then you hear a lot of criticism about the engine and the noise.
"I was out for an event in the afternoon and DC [David Coulthard] drove the old V8 [a Red Bull], and it made a sound. There was nothing you could say against it.
"In general, I would say F1 is the pinnacle of motor sport, it is not GP2, and therefore it is the right step."
Pressed on whether the sound could be raised, Wolff added: "I'm not too much of a technician, but I think we need to look into things.
"If we agree there should be work done on sound then we should look into it. Whether it is possible, or whether it is the right step, I'm not sure," he said.
-Independent