Cook (104no) completed his first Ashes hundred since his glorious 2010/11 campaign, just before the close on day two at the MCG, to help the tourists to 194-2 in reply to 327 all out.
Broad had earlier almost doubled his series wicket tally with 4-51 as two of England’s blue-chip performers found their form at last to try to stave off a 5-0 whitewash.
Former Ashes-winning England captain Michael Vaughan was among those who have questioned the lynchpin seamer’s place of late.
“I’ve had one of those weeks where you get your tin hat on, duck down, and don’t see much,” said Broad, after taking his career wickets column to 397.
“I’ve been unaware of what’s written, what’s been said. You have to go to that place as a sportsman, find something within yourself, get support from people around you, and build yourself back up.
“You can get yourself in a dark place if you read everything.”
Broad will bear no grudges against Vaughan or anyone else paid to have a high-profile opinion - as he admits he may well be himself one day.
“Only two weeks ago, I was on holiday with him ... (but) I think people just do their jobs and have to be critical at times, and I deserved criticism after the Perth defeat for sure.
“I won’t hold any grudges or get disappointed if people slag me off, because in 15 years’ time I might be doing the same ... not six months!”
Cook too has had his critics of late, after a run of poor form at odds with his status as national record runscorer.
“In the changing room, the celebrations when he got that hundred were huge,” said Broad. “That’s testament to the way he is.
“He went through so much stuff with his captaincy that I’m not sure a bit of stick about not getting runs is going to bother him too much.”
Both had to dig deep to prove their mettle - even if it has come too late to hang on to the urn.
“I think it shows a huge amount of character to be under that sort of scrutiny and pressure and come out and deliver any sort of performance - let alone a hundred, like Cookie has just done,” said Broad.
“I don’t think you play this amount of international sport without some sort of deep inner self-confidence that you can find when you’re very low. You have something there you can clutch on to when things get tough.”
Broad admits he under-performed in the innings defeat which handed Australia an unassailable 3-0 lead last week.
“I thought I bowled pretty well at Brisbane and okay at Adelaide, but Perth obviously very poor,” he added. “At the WACA I fell into a mental trap of being too defensive ... looking not to concede runs, instead of looking to take wickets.
“I need that mentality as a bowler - ‘Where’s my next wicket coming from?’ - not ‘Where am I going to stop the next boundary?’.”
Australia off-spinner Nathan Lyon was happy to give due credit to both Cook and Broad.
He said: “You always know there is world class in that opposition changing room - they have absolute superstars in there - so there was going to be a time in this series that they all stand up.”