England's familiar frailties were in evidence again on the final morning as some more weak dismissals saw them bowled out for 312 in their second innings to slip to a 218-run defeat in Adelaide.
That left England, who beat the same opposition 3-0 in England in the summer, 2-0 down with three to play, and a daunting trip to Perth coming up next.
Cook told Sky Sports 2 England were not down and out, saying: "We've had a big hit and if we believe that the Ashes are gone, they might as well be gone.
"We've had two tough games and we haven't played well. That's the simple deal.
"We have to dust ourselves off and do what we can do, which is work bloody hard on our games and come out to Perth on Friday with that belief that we can do something. We need to put some pressure back on Australia."
Cook was at a loss to explain what has gone wrong for England in such a short space of time.
"I don't know what's quite gone on these couple of games," he said. "We feel we're doing the right things but at the moment our skills in the middle are letting us down.
"We're not scoring enough runs, we're not taking our chances.
"The only people who can change that are the 16, 17 players in the dressing room.
"I've got to step up as a batter and score more runs. Everyone has to.
"You always start asking questions about the side when you lose a couple of games. It happens in every sport.
"What we do know is that side has got a lot of talent, a lot of skill and has proven that over a long period of time. We have to hold on to that.
"We are very good players in that dressing room, but you can only say that for so long and we have to start delivering."
With a number of players repeatedly getting out in a similar fashion, Cook added: "That's an area of concern: shot selection and shot execution. We can't shy away from that, some poor shots have been played.
"That's honest, and we have to be better than that if we want to get back into this series."
He continued: "We have to look hard into ourselves, deep into the inner soul and drag the performance out of ourselves. A 2-0 lead is not insurmountable. I remember turning up in Manchester (in the summer), and the pressure can change because you're so close.
"It's a bit like football - if we get the next goal, it's vital.
"We can't mope about feeling sorry for ourselves. We have to hold our hands up and say we haven't been good enough. We have to drag the runs out of ourselves, drag the wickets out of ourselves."
On the absence of Jonathan Trott, he said: "When you lose a guy with that experience and that class, that kind of experience is very hard to replace. Having said that (Joe) Root played very well. Little things like that we have to draw on."
Australia captain Michael Clarke dismissed the idea the wins have been easy.
"It's still the hardest game it the world," he said. "It's enjoyable, there's no doubt about it. The thing that's most pleasing is we're finally getting the results."