The former midfielder, who retired in February due to repeated concussions, has joined the Demons' coaching staff in a part-time role, predominantly working from the bench on match days.
Brayshaw, 28, was on the Demons' bench for the first time as a coach in Sunday's 45-point win over the Western Bulldogs at the MCG.
"He's going to be just dipping his toe into some of the part-time work later in the week," Goodwin said.
"He wants to be around our group and obviously on game day, just helping bench coaching.
"He brings enormous energy to our club and today was the first step of that and we'll just continue to assess what that looks like.
"It was his first crack so he was good. He was very positive down there, which is what you want.
"Yeah, we want our players heading to the field in a real positive mindset because that's when people really grow."
Goodwin said he would "debrief" with Brayshaw over a coffee later in the week.
Brayshaw's coaching role isn't related to his playing contract.
The AFL will need to make a decision on whether Brayshaw's salary, expected to be paid out in full, will be included in Melbourne's salary cap or exempt.
There were plenty of blue helmets among Melbourne fans in the crowd on Sunday in tribute to Brayshaw's career.
"Angus today is a big part of our footy club," Goodwin said.
"We love what he brings at our footy club, we have for a long, long time and he's an important person to us.
"It's great that our supporters can show what Angus means to them.
"We've got a little award that we present internally, the 'Demon Spirit' award, we have that (Brayshaw's) helmet as part of our journey for this year.
"And our supporters have obviously bought into that."
Goodwin said it was "a bit too much" to suggest Melbourne were dedicating their season to the midfielder.
"But there's certainly a legacy that he's left with our club," he added.
"There's a legacy that he's been able to leave around our culture, the way we go about our business, the way we train, the way we drive standards, the way we perform.
"And he's a big part of that, he's left a legacy and we want to honour that."
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