Cook presided over a dismal 5-0 Ashes whitewash defeat, which concluded in the early hours of Sunday morning UK time as Australia wrapped up a three-day win in Sydney in which they twice bowled out the tourists for under 200.
Hussain could barely contain his anger afterwards, and questioned Cook's decision-making and his authority over the team.
He told Sky Sports 2: "Over this series, he has been completely and utterly out-captained by Michael Clarke. He hasn't learnt one iota from first game to last.
"The field settings, the plans - when Brad Haddin comes in, they go to short stuff - England haven't learnt a single thing. It's been absolutely abysmal.
"He's got to start proving to people that he is willing to learn as an England captain.
"He's got to stand up to people - stand up to Jimmy Anderson and say, 'Do you know what? In four years' time, they won't say it was Jimmy Anderson that lost this tour 5-0, they'll say it was Alastair Cook's tour'. Say that to (Stuart) Broad.
"Take command of your own game, your own gut feeling. If you don't have one, give the job to someone else.
"He's shown with the rest of his game that he can learn and this summer he's got to show that to England fans, management, players, everyone.
"Andrew Strauss, in 2006(-07) when they lost 5-0, vowed to himself that he would never let it happen again. Cook must make that promise to himself that he will not let this shambles of a tour happen again."
Former England batsman Paul Collingwood, though, backed Cook to learn the necessary lessons.
"Alastair Cook has done a great job for England, he's obviously got good leadership qualities," he said of a captain who had won or drawn his five previous series in charge.
"Cook will hold his hands up that Clarke has had a better series than him but he is always learning. I'm sure he is the right man for the job, he has to have that determination to put things right in the future."
There was widespread dismay at England's capitulation and a nother former captain, Michael Vaughan, told BBC Sport: "I've lost words to describe how England played.
"That was pathetic - it was always going to happen but there's a way to lose. I have never seen an England team throw in the towel, but they did this afternoon. That last innings there showed how frazzled the team is."
Former England opener Geoff Boycott agreed: "It's pathetic - there is no other word. It's humiliation.
"This is a worse loss than when we lost before 5-0 because they had great players like (Glenn) McGrath, (Shane) Warne and (Adam) Gilchrist last time. England have just disintegrated."
Former Test all-rounder Ian Botham described England's performance as "spineless" and believes the lower order in particular were frightened by the pace of Mitchell Johnson, who took 37 wickets in the series at an average of less than 14 runs.
Botham told Sky Sports: "I'm pretty depressed and embarrassed - I use that word, embarrassed, and I mean it.
"I am not allowed to use the words that are flashing through my head. I just think it was spineless.
"It's the fear factor of Mitchell Johnson. You expect to see the late middle-order and the tail contributing with the bat. It hasn't happened - t hey've been blown away, they've been startled rabbits, they've been hopping about, fending it off.
"They've had a wake-up call. They probably haven't faced someone bowling at 90mph for quite some time - that's the way it appeared, anyway. That's the scary part for me."
Johnson dominated the series the way Botham himself did in 1981, and Collingwood believes his contribution will be remembered in equally reverential terms.
Collingwood told BBC Radio Five Live: "Mitchell Johnson was fantastic, the impact he had throughout the series was incredible. We have heard about 'Botham's Ashes' in the past but this could easily be called 'Johnson's Ashes'."
Botham at least saw a silver lining in the emergence of all-rounder Ben Stokes, who made 120 at Perth and took six for 99 in Sydney, and wants further new faces to follow the Durham player into the side.
"I think England have got to grasp this now and say 'okay, we've got some really hard thinking to do'," he said.
"I'm not talking about a mass cull but they've got to start looking at some of these younger players. Ben Stokes came into the side and was a breath of fresh air. There has got to be a few more of those out there."