Dogs defender Cleary was knocked out when Archer's knee made contact with his head in a contest in Saturday night's match at Marvel Stadium.
Play was stopped and Cleary received medical attention before being taken to hospital.
The 23-year-old was back at Whitten Oval in good spirits on Monday but will miss the Bulldogs' AFL/VFL centenary celebration match against Collingwood on Friday night under concussion protocols.
The match review officer graded Archer's actions as careless conduct, severe impact and high contact, resulting in a three-game suspension.
North Melbourne on Monday confirmed they will challenge the penalty at the tribunal.
If it stands, Archer will miss games against Melbourne, Adelaide and Sydney.
Former Bulldogs captain Murphy, who has returned to the club in a leadership and cultural capacity this year, does not believe Archer should be suspended.
"Because there wasn't a lot of replays on the night it was sort of hard to judge, but my initial thought was it was just one of those unfortunate accidents," Murphy said on Monday.
"We get the luxury of looking at it in slow motion, and it's whether the tribunal thinks he had another option, and they might deem that he did.
"There's definitely no malice and it's one of those ones where you don't want to see players miss footy for those sort of things, but it may end up that way."
St Kilda great Nick Riewoldt said he would be "really fearful for the game itself" if Archer, the son of North Melbourne legend Glenn Archer, was banned over the collision.
"You can't legislate accidents out of the game," Riewoldt said on Triple M.
"We don't want concussions, that point has been made, that's why players that are now bracing and protecting themselves are getting suspended.
"Jackson Archer is lucky not to have a broken leg. It's a violent collision.
"North has to appeal this decision. I would be sad if he doesn't get off this."
Bulldogs midfielder Tom Liberatore, standing in as captain while Marcus Bontempelli is injured, didn't want to buy into the debate around Archer's suspension.
"I honestly haven't really thought that much about it," Liberatore said.
"My main concern is Luke and that's up to the match review panel."
Liberatore said he is "pretty clear" on how to attack contests, despite ongoing uncertainty about how accidental collisions will be judged.
The hard-nosed veteran said Cleary had recovered well from the "pretty bad collision" with Archer.
"He was in hospital overnight Saturday and I checked in with his family and checked in with him," Liberatore said.
"He's in (at the club) today and he's actually recovered quite well."
Archer's case is one of three set to be taken to the tribunal this week.
Hawthorn will challenge defender Jack Scrimshaw's three-match ban for a high hit on Essendon's Jordan Ridley, and Richmond will challenge Tom Lynch's one-match suspension for rough conduct on Carlton's Tom De Koning.
Sydney have accepted Justin McInerney's three-match ban for the bump that concussed Brisbane's Brandon Starcevich.
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