The England captain was unable to resume his innings immediately on the final morning of the series, having arrived at the SCG after being treated for vomiting and diarrhoea.
Steve Smith's 687 runs were one clear point of difference between the two sides in the Ashes but the Australia captain was happier to talk about his bowlers after wrapping up a 4-0 series triumph on Monday.
Australia's bowling quartet - Mitchell Starc, Pat Cummins, Josh Hazlewood and Nathan Lyon all picked up 20 wickets each in the series and with the win, the Aussies have regained the Ashes urn.
The team also had to contend with off-field distractions (Ben Stokes absence, Jonny Bairstow's (in) famous headbutt) and overall it painted a very poor picture of England cricket's hierarchy and structure.
He said: "I think England had their foot in the door in all of the Test matches, they've played some exceptional cricket and we've just been able to get on top in those key moments and not let them back in the game which has been crucial".
The damage was minimal, with Cook undone on 10 by a attractive delivery from Nathan Lyon that turned sharply and hit the top of off stump.
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Dawid Malan followed when Lyon trapped him leg before wicket for five.
Australia haven't batted for so long in a Test dig since 1997, when Steve Waugh and Greg Blewett helped the tourists frustrate South Africa for 193.4 overs in Johannesburg.
Mitchell Marsh was bowled next ball by Tom Curran for 101 off 141 balls with 15 fours and two sixes.
Among his innings, Smith made a superb 239 during the third Test in Perth.
Earlier, Shaun Marsh was run out for 156 following a mix-up with Tim Paine after lunch.
Big-hearted paceman James Anderson bowled with great economy in the stifling conditions as temperatures hit 42 Celsius (108 Farenheit), taking one for 56 off 34 overs.