Evans and coach James Hird made emotional speeches on Monday night at the Bombers' season launch, thanking the players and fans for their support.
Captain Jobe Watson also took to the stage, saying the players could sleep comfortably knowing what they had and had not done.
The club is under a joint Australian Sports Anti-Doping Authority and AFL investigation for supplements that the players used last season.
Evans has also announced an independent review of the club as a result of the crisis.
The anti-doping investigation is likely to take months, meaning it will hang over the Bombers for much of the season.
"I understand the way you look at me tonight, looking for reassurance our beautiful place will be okay," Evans said.
"I promise you that it will be.
"The hurt of the past few weeks is still raw, but it is this room that gives me strength - given how you all have stood behind the club in its hour of need.
"We will get through this and we will be a better, stronger organisation."
Evans also apologised for the circumstances that led to the crisis.
"Mistakes have been made and I sincerely apologise that they have occurred," he said.
"We will get to the bottom of what happened, we will make sure those mistakes never happen again.
"While we know some things, there is so much we don't know, and we're continuing to piece together a long and complicated jigsaw puzzle.
"I commit to you that we are making progress."
Hird said it had been humbling to coach the team in the past few weeks, adding the players had stayed focused and disciplined.
"My family and this football club means everything to me and I will do everything that is in my power to get the club through this difficult time," he said.
"That means being the best coach I can be to this wonderful team of young men who wear our colours so proudly."
Evans has also announced an independent review of the club as a result of the crisis.
The anti-doping investigation is likely to take months, meaning it will hang over the Bombers for much of the season.
"I understand the way you look at me tonight, looking for reassurance our beautiful place will be okay," Evans said.
"I promise you that it will be.
"The hurt of the past few weeks is still raw, but it is this room that gives me strength - given how you all have stood behind the club in its hour of need.
"We will get through this and we will be a better, stronger organisation."
Evans also apologised for the circumstances that led to the crisis.
"Mistakes have been made and I sincerely apologise that they have occurred," he said.
"We will get to the bottom of what happened, we will make sure those mistakes never happen again.
"While we know some things, there is so much we don't know, and we're continuing to piece together a long and complicated jigsaw puzzle.
"I commit to you that we are making progress."
Hird said it had been humbling to coach the team in the past few weeks, adding the players had stayed focused and disciplined.
"My family and this football club means everything to me and I will do everything that is in my power to get the club through this difficult time," he said.
"That means being the best coach I can be to this wonderful team of young men who wear our colours so proudly."
Watson described the strain of the last month on the players.
"I think certainly the players feel the pressure. It's around you wherever you are," Watson said.
"For probably a two-week period it was a total saturation of your life and probably the footy club was the sanctuary, and being around each other was the release."
Watson said the players had been galvanised by the controversy and that the return of games had given them something to push their energy towards.
Alluding to the investigation, Watson's words were profound.
"Each player in terms of his value system and what you know to be right and wrong, when facing this kind of situation, you know what you've done and what you haven't done," last year's Brownlow medallist said.
"And so I think every player can comfortably go to bed at night knowing how they feel about that."
The night ended with champion forward pair Matthew Lloyd and Scott Lucas inducted to Essendon's Hall of Fame, with Lloyd going straight in as a legend.
Lloyd, the club's leading goalkicker and a star of the 2000 premiership team, won three Coleman Medals and was a five-time All Australian before retiring at the end of 2009.
Lucas played 270 games, like Lloyd, and was also a member of the 2000 premiership team. The long kicking left-footer also won two best-and-fairest awards, one as his team's centre half-back.
Others recognised at the event were former premiership players Roy McConnell, Fred Baring and Darryl Gerlach.
Former No.1 ticket holder Bruce Heymanson, who died in January, and Bill Brew, a long-term committeeman, were also inducted, Brew as a legend.
