Reassuring responses all round convinced him that, even from 2-0 down with three to play, England move on to Perth still capable of battling back to win the series.
It is a long shot, of course, to pull off a feat achieved only once; 77 years ago, and then by Australia, not England.
Cook knows England got exactly what they deserved, and can hardly argue otherwise after twice being blown away by the pace of Mitchell Johnson.
"Sometimes, when you haven't been playing well, that's one thing you start looking at - whether we do have that," he said. "I can only say - from speaking to the guys, and watching them, how much this is hurting - that we do. Only the guys will know that inside themselves. But I honestly believe we've got that.
"We've been outplayed . . . you can't get away from that. But the only way we can drag it out is by getting that hunger, that desperation back into our game."
As for his own state of mind, as he approaches his landmark 100th Test in Perth on Friday, Cook does not try to disguise the impact of two crushing defeats.
"I think that's part and parcel of the job. There are some very tough moments for the captain, and we're in the middle of it. We're 2-0 down, and I'm responsible as the captain for that. Yes, it does hit you hard. It's how you bounce back. Sport shows what character you can be."