The two-time North Melbourne premiership coach, who previously coached the Bombers' reserves, has also reflected on his own fateful decision to go to Carlton, calling it the biggest regret of his career in football.
Referring to his tumultuous time with the Blues, Pagan said it was impossible to achieve success without unity at a club.
The Bombers are at one of the lowest ebbs in their history, sacking coach Ben Rutten a week ago after a barren season.
Chairman Paul Brasher and half their board have also left, along with chief executive Xavier Campbell.
As the Bombers look for a new coach, Pagan has backed Lyon and Williams.
Williams coached Port Adelaide to their only premiership and Lyon led St Kilda to within one kind bounce of their second premiership, before taking Fremantle to their only grand final.
Neither Williams nor Lyon are seen now as leading senior coaching candidates, but Pagan has backed them to have the right effect at Essendon.
"Having known both those guys pretty well, I reckon they'd do a really good job," Pagan told Nine's The Footy Show.
"If you get one of them, I reckon they're taking a step forward.
"For the first five years when you're coaching at senior level, all you're really doing is practising on the players.
"You don't want anyone practising on the players at Essendon."
Pagan was reserves coach at Essendon in the early '90s before he went to North.
"Essendon were a great club ... but gee, they look a real shambles at the moment," he said.
"They have to make some decisions and they have to be the right decisions - and provide a good foundation before they can go forward."
Pagan was similarly candid about Carlton, where he went in 2003 after leaving the Kangaroos.
The Blues were reeling from their heavy AFL penalties for salary cap breaches and they never made the top eight before his 2007 sacking.
Asked if going there was his biggest regret, Pagan replied: "Without any doubt whatsoever."
"I wish I had picked another club," he said. "It was just a nightmare a minute.
"It was, for want of a better expression, a snake pit.
"It was like going into work every day and a little bloke hiding behind the door with a sledgehammer and whacking you under the chin."
But Pagan, now a Group 1 winning horse trainer, is rapt at their progress under current coach Michael Voss.
"I would have loved to have been coaching the team they have now," he said.
He similarly praised North president Sonja Hood and the club for snaring new coach Alastair Clarkson, calling it "an amazing achievement".
Pagan said he had "a couple of chats" with Hood, who picked his brains as they pursued the four-time Hawthorn premiership coach.
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