England slipped to an eight-wicket defeat at the MCG on Sunday to go 4-0 down in the Ashes series and are now staring down the barrel of a whitewash in Australia.
Cook struggled for runs in the summer when he successfully guided England to a third consecutive Ashes victory but that now all seems a long time ago as he continues to look for fluency at the top of the order.
And Vaughan questioned Cook's tactics during the Melbourne Test, with the decision to bowl Joe Root ahead of front-line spinner Monty Panesar on day four raising a few eyebrows.
"He's under huge pressure because his team are 4-0 down," former skipper Vaughan told BBC Radio Five Live
"I hope he sticks with it, I hope he learns from a lot of mistakes that he made, particularly on the fourth day.
"He got his tactics wrong on the third morning when (Nathan) Lyon and (Brad) Haddin came out. He just spread the field, England only needed one wicket and he just allowed momentum to go Australia's way.
"On the fourth morning, to take Stuart Broad off after the second over, to not bowl Monty Panesar, then to spread the field.
"You feel that he's got a long way to go in terms of making sure that his tactics improve."
Vaughan was also quick to question the role of the senior England players and coaches, suggesting that they should give Cook more support as he grows into leading his country.
"I'd like to know what the senior players in the team are doing," he added. "You've got guys out there who have played 100 Test matches in Kevin Pietersen, you've got Stuart Broad. The senior bowler, Jimmy Anderson, has played many many Test matches.
"What are they doing on the tactics? Why aren't they helping him out? Where are the coaches on the team? Why aren't they delivering more of a thought process in terms of making sure the tactics improve.
"So far in this series, I don't think anything of England's form or batting or bowling or fielding or planning or training has been anywhere near the standard of what I would expect from an England side."
Another former England opener in Geoffrey Boycott believes Cook's position as captain will come under greater scrutiny if he cannot improve his own personal form.
The 29-year-old has reached 50 in the last two Tests but is still well below his, admittedly lofty, usual standards and Boycott feels that will add to the pressure on his shoulders.
"I don't think he can fall back on other things that some other captains I've played under had," he said.
"It's not just this one match because when you're losing, everything is highlighted."
Boycott did not lay the blame for England's failure on tour at the door of Cook, however, stressing that inadequacies all-round had contributed to their problems.
"They've made a mess of everything," he said.
"In fact, they've got to the point where it doesn't matter where any of them bat, they're going to get out and they're not going to win because they are shot.
"Mentally, physically, they're just down, their spirit is broken."
Former England spinner John Emburey was critical of the leadership on the tour and encouraged Cook to be more forthright on the field.
"I don't think we've been well led in this series," he said.
"It's easy to blame Alastair Cook, we've got a lot of people in the background and the experienced players in (coach) Andy Flower, (batting coach) Graham Gooch.
"What are they getting into his head? He's got to be out there. He's got to be leading this side, both in the dressing room and on the field.
"It's important that it reflects on him so everything that happens out there has got to be him. I hope there's not too much influences coming from off-field in things that he's doing on the field."