At the Melbourne Cricket Ground on Sunday, England suffered their most dispiriting test defeat so far in this Ashes series - surrendering a first innings lead of 51, enduring two big second innings batting collapses and eventually losing the match by eight wickets with more than a day to spare. (Agencies)
"The bottom line is we haven't been good enough," Cook told reporters. "The part of this game that makes it even more frustrating is that we got ourselves into a good place to put some pressure on Australia."
Australia were chasing a record 231-run victory target at the venue since drop-in pitches were first used at the Melbourne Cricket Ground in 1996 and yet they won by a distance.
Given England were in control of the match at the end of day two with nine Australian wickets down and the home side 91 runs behind England's first innings total, this must count as the tourists' lowest point on the tour.
"It's very disappointing. We worked very hard for two-and-a-half days to get ourselves in that situation. When you don't follow it through, it hurts even more," Cook said.
Unfortunately for England, Cook's captaincy was uninspiring to say the least.
At the start of day three in Melbourne when England required one wicket and Australia were under pressure, Cook took his all-too-common cautious approach.
With Brad Haddin the only recognised batsman at the crease batting with the number 11 Nathan Lyon, Cook inexplicably decided to protect the boundaries and get his bowlers to bowl short, despite their lead.
Cook's aberrations continued on Sunday when he dropped two chances at first slip.
The second drop was as easy as they come off David Warner's blade. It cost England only two runs as Warner was caught behind a few balls later but hinted at a captain with a scrambled mind.
The first chance was tougher and a result of confusion between Cook and wicketkeeper Jonny Bairstow that allowed Chris Rogers, then on 19, to carry on and hit a match-winning 116.
Astonishingly, Stuart Broad, who induced that Rogers edge during a spell when he was bowling with fluency and threat, was taken off and not seen again until 20 minutes before lunch.
To baffle further, Cook ignored his front-line spinner Monty Panesar until 25 minutes before lunch, preferring instead to bowl part-time off-spinner Joe Root.
"The reason Rooty came on ... was two left-handers, and the drift with the wind. It would have been counter-productive with Monty bowling at that end with the drift," Cook explained.
"As always, with a captain, you make that decision at the time - and I'm sure there's a lot of people who might have done it a different way."
A fourth successive defeat has left England with a selection conundrum - whether to show faith in the team that failed so miserably or risk a repeat of the selection lottery that blighted them for much of the 1990s.
Their bowlers have battled hard, even if they got completely overshadowed by the express pace of Australia paceman Mitchell Johnson.
No matter how good they are, they cannot create pressure if their batsmen continue to perform as turgidly as they have done in the series so far.
Their second innings capitulation for 179 underlined deep flaws running through a lineup that appeared uncomfortable against Johnson and unsettled by the loss of Jonathan Trott who abruptly returned home to deal with stress-related illness.
With Root shifted up to three to fill the void, Ben Stokes battling at six and Bairstow failing to cover for the dropped Matt Prior, Cook's options are limited.
Yorkshire's Gary Ballance is waiting in the wings but it may not be a good idea to shoehorn a rookie into a team so dishevelled and bereft of confidence.
Cook was resolute about only one selection. "I'm 100 percent wanting to carry on," he said.
"If someone makes that decision, and says 'we think there's a better man' or 'you're not good enough to do it' then I have to take that on the chin - because as a captain, you're responsible for the team," he said.
At the Melbourne Cricket Ground on Sunday, England suffered their most dispiriting test defeat so far in this Ashes series - surrendering a first innings lead of 51, enduring two big second innings batting collapses and eventually losing the match by eight wickets with more than a day to spare.