Cook's men arrived as favourites to retain the Ashes with a fourth successive series win over hosts Australia but have already relinquished the urn and were rocked further with the shock retirement of spearhead spinner Graeme Swann on Monday.
The England captain, who celebrated his 29th birthday on Wednesday, will be forced to reshuffle his bowling attack following Swann's departure but was keen to look for positives ahead of Thursday's match after a woeful tour to date.
"It's been an interesting week," Cook told reporters in Melbourne on Wednesday with his England side already 3-0 down in the five-test series after heavy defeats in Brisbane, Adelaide and Perth.
"Losing the Ashes and with Swannie going as well, it has been a different week.
"When you lose games of cricket, naturally your confidence does slip."
Monty Panesar is expected to come in for Swann while pace bowlers Jimmy Anderson and Stuart Broad are battling against a loss of form and a foot injury respectively.
Wicketkeeper Matt Prior could also miss out due to a poor run of form with the bat and recent problems with the gloves but Cook insists that whoever lines up for England in Melbourne will be united in their quest for redemption in the series.
"We're desperate to turn it around and you don't often get the chance to play a Boxing Day Test match at the MCG, which reportedly is going to be pretty much sold out for the first day," the left-handed opener added.
"That's an incredible opportunity we have as players. We know we're up against it in terms of the last three results.
"But you've got to keep believing in yourself."
Cook praised Swann's contribution to the England side over the past five years and was keen to emphasise the spinner's comments in a news conference on Tuesday accusing some international players of "disappearing up their own backsides" were not aimed at any of the current touring squad.
"A phone call to Swannie reassured me very quickly that it wasn't at all about any of the England players," Cook added.
"He totally 100 percent reassures me and the whole England team that it's not about us. So to me, the matter's closed on that."