The former Carlton forward joined the Lions in late 2009 but was sacked by the club on Sunday evening after repeatedly breaching the players' code of conduct.
"Whenever you recruit a player, you recruit them on the premise that they can make you better," Voss told a packed media conference in Brisbane.
"That's what we hoped to get and clearly we didn't get that, so for us, I can't sit here and say it wasn't a mistake because he's now left our football club.
"But it's important to also realise that you can't make two [mistakes]. That's why this decision needs to be made and I'm fully supportive, absolutely, of what the board has done."
The last straw for the Lions was Fevola's drunken antics on New Year's Eve. On that night he was arrested at 4.30am after a scuffle with police.
While he subsequently checked himself into a rehabilitation facility, where he continues to be treated for a range of problems including depression, Lions chairman Angus Johnson said Fevola had to be axed "to uphold the culture and reputation of our football club."
Johnson added: "The club has … lost confidence in Brendan's ability to meet his obligations as an AFL player due to these persistent breaches.
"Brendan was informed of that decision last night. The timing of the decision was the result of medical advice that strongly indicated it was in the best interests of Brendan's health and wellbeing to notify him immediately.
"Brendan's health and wellbeing have been the club's primary focus throughout this period."
The Lions have begun negotiations with Fevola's management, as the two parties attempt to reach a financial settlement.
The 2006 and 2009 Coleman Medallist had two years left on his contract, during which time he was set to earn an estimated $1.9 million.
"While Brendan will no longer be a part of our playing group, the club will not be abandoning him," Johnson said.
"We will provide assistant to Brendan that will provide him with an opportunity to obtain the necessary treatment required to maintain his health.
"This should also allow Brendan to prepare for his future life."
Johnson had a one last stinging message for Fevola.
"Ultimately, individuals also have to take responsibility for their actions and accept the consequences when they fail to meet standards set by their club and teammates," the chairman said.
"Make no mistake, this was an extremely difficult decision but we believe it to be the right decision."
