In a startling claim, World Anti-Doping Association president John Fahey said last week that it was "only a matter of when" the Bombers players would be handed infraction notices.
He later backed away from the claim, but it again raised the spectre of player sanctions.
But instead of dreading the possible consequences, Stanton said the players were focusing on preparing for 2014.
"As you've probably heard about a million times, it's an ongoing process and we'll deal with whatever comes our way when it happens," Stanton said at the club's True Value Solar training base at Tullamarine on Wednesday morning.
"We're not too worried about it at the moment. We're training and we're getting prepared for a new season.
"But it's an ongoing process and we'll respect that, and that's all I can really say."
Essendon has already been investigated by the AFL and ASADA for its use of supplements in 2011-12, but the investigation remains open for possible further penalties.
The club was fined $2 million, coach James Hird stood down for 12 months, football manager Danny Corcoran suspended, assistant coach Mark Thompson was fined and draft picks were taken away.
Stanton and his teammates took part in an open training session in front of hundreds of fans at the newly upgraded training centre on Wednesday.
The pre-Christmas session had a festive feel, with provided jumping castles for the kids, food tents and ice cream vendors operating beside the ground and music blaring out of speakers.
Stanton said the players were keen to put a difficult year behind them.
"We're looking forward. It's a brand new season coming next year, and it's been a big year," he said.
"But I think the boys have really grown, in terms of the way they've handled themselves on and off the field.
"It's been fantastic that this football club has been able to grow and, you can see out here today, the fans have really come out to support us and we really thank them for that.
"We've tried to do our best on the field and we'll keep developing ourselves off the field as well – and I think that's an important lesson coming out of this year."
Twitter: @AFL_BenGuthrie
