There have been suggestions Bombers players could still be gaining an advantage from supplements allegedly used last year, despite no conclusion from ASADA that they have done anything wrong.
"There appears to be a small group, particularly amongst our clubs, who are taking it upon themselves to put about scurrilous innuendo about the fact that the Essendon football club has won five games, and are they getting an advantage?" Demetriou told Melbourne radio station 3AW.
"The sooner some of our clubs - and this is not all but a small few - stop this scurrilous (rumour) mongering, the better," he told.
"It just might be that they've got some good players, it just might be that they’ve got some good tactics, it just might be that their coach is coaching well, they might actually just be playing well.
"(The critics) should focus on their own club."
"I think this is really unfortunate, I think it's a by-product of this running commentary and I don't think it is acceptable and it just might be that they've got some good players."
It has also emerged Carlton officials had been conducting their own investigations about the Bombers' fitness program.
Essendon remains undefeated heading into Saturday's game against GWS.
Bombers players are expected to be interviewed by ASADA investigators as early as next week.
Coach James Hird said on Friday he'd be surprised if his players were distracted by the interviews.
The release of an independent report completed by former Telstra boss Ziggy Switkowski has been delayed for legal reasons.
Matt Thompson is a reporter for AFL Media. Follow him on Twitter @MattThompsonAFL
