Brown was offered separate two-week bans by the Match Review Panel for his high hits on Callan Ward and Barry Hall that McKenna said had clearly crossed the line.
The former Hawk risked a five-week sanction if he had contested the charges at the Tribunal, but a disappointed McKenna said Brown had taken responsibility for his actions and was now focussed on repairing the damage done.
"I spoke to him over the course of the weekend and he addressed the playing group today and was obviously remorseful," McKenna said on Tuesday.
"He understands he's let them down and he's got to earn back their trust.
"He's the deputy vice-captain … and we like to think that not just our leaders, but our players, make good decisions on and off the field and he's got to earn back that trust which I'm sure he'll do.
"One of the things when we recruited Brownie was because of his hardness and his attack on the football and he was part of a modern-day defence at Hawthorn, but we want to play hard and fair.
"The rules are quite clear and unfortunately he's crossed that line and he takes his medicine and we move on."
McKenna said he was comfortable with the penalty handed down by the MRP and disputed the notion it should have been more sever, as some media outlets speculated.
The youthful Suns will attempt to register their first AFL win against Melbourne at the Gabba on Sunday with Brown's suspension leaving a big hole for McKenna to fill in defence.
"He was just starting to run across the ground after an interrupted pre-season," the coach said.
"He's certainly part of the glue that binds our defence together alongside Nathan Bock. His leadership and his hardness will be sorely missed."
Gold Coast skipper Gary Ablett defended his teammate's passion on One HD show One Week at a Time on Monday night, but agreed he would need to temper his aggression in the future.
Ablett has also attracted some criticism for the amount of time he has spent in Melbourne since joining the fledgling club.
Hawthorn president Jeff Kennett recently made a veiled reference to Ablett's situation in his regular column on the Hawks' official website, but McKenna dismissed suggestions his skipper was anything less than 100 per cent committed to his new club.
"With those comments you sort of sit back and giggle a bit because we know what Gary's workload is during the week and during the months in pre-season," he said.
"We've got a tab on who's been down in Melbourne more than most and Gary's certainly not on the top of that list.
"He is from Melbourne and we are an interstate club. We like to look after our players as best we can and we'll afford them as much time as they have to to get back and see family and friends if that's what keeps them happy.
"There are probably more players who have been spending more time back in Melbourne than what Gary has."
