The Bombers opened the season on Friday night with a stirring 35-point away win over Adelaide.
That was six weeks after they became the subject of a joint Australian Sports Anti-Doping Authority and AFL investigation for supplements given to the players last season.
Zaharakis said one effect of the ongoing scrutiny was that the players were spending more time in each other's company.
"We were a pretty close group before this, but over the last six weeks we've pretty much only spent time with the boys around the club, because that's your escape (from the public scrutiny)," he told Channel Seven's Game Day.
He added Friday night's win was a massive result for the club.
"It was worth more than just the four points.
"We didn't shy away from it during the week - Hirdy spoke about the last six weeks and the ordeal of it all.
"It was definitely a big win.
Zaharakis also expressed guarded confidence that the investigations would clear the club.
"I can only speak for myself ... but you're confident in the processes that were taking in place at the time," he said.
But Zaharakis admits the saga has been difficult with the children of some Essendon coaches and players being bullied at school.
"Definitely, it takes its toll on everyone and it's ridiculous people can start targeting your family or your kids," he said.
"I know some of the coaches and even players who have kids at school, (those children) have copped a bit of bullying."
Former Essendon player Mark McVeigh, a long-time friend of James Hird, said the Bombers coach was clearly showing signs of stress.
"Looking at James, he's lost a bit of weight," McVeigh said.
"No doubt, he looks a little bit stressed and it's taken a toll on him.
"He's a resilient person, a great figure of the game.
"It would have taken all of his strength to get himself up, to get the club in the right frame of mind to be able to play."
Meanwhile, Zaharakis expects to play in the VFL next weekend to gain match fitness.
He was Essendon's substitute on Friday night and the Bombers now have a week off ahead of their next game against Melbourne.