Cook presided over a disastrous winter tour of Australia and the fallout has seen several personnel changes in the England camp, with the most notable being Peter Moores becoming head coach following Andy Flower's decision to step down.
While Cook clung on to his job as Test and one-day skipper, he has been partly responsible for the decisions to dispense with the services of controversial batsman Kevin Pietersen and batting coach Graham Gooch.
Therefore, Vaughan believes Cook will feel more burdened to succeed against Sri Lanka and India this summer.
"The pressure is on him. Any failure, any disappointment will be jumped on by a lot of people," Vaughan, who skippered England in 51 Tests from 2003 until 2008, told BBC Sport.
"Even though he's won an Ashes and won in India, Cook will probably feel like this is a fresh start, what he's going to be judged on as an England captain.
"He has made some tough calls. He has got rid of his best pal - batting coach Graham Gooch - although I believe it was a management decision and a Peter Moores coaching decision as much as Alastair Cook's.
"He has got rid of the man who has scored more runs for England than anyone else in Kevin Pietersen so, although the public will be behind him, there will also be more pressure on the England side."
Former off-spinner Graeme Swann, who retired midway through the 5-0 Ashes whitewash after the third Test in Perth, believes it is crucial for the team to start building momentum as soon as possible, starting with the limited overs matches against Sri Lanka.
"Alastair Cook will be desperate for a couple of new heroes to emerge and really stamp their names on proceedings for the summer and become the new faces of English cricket," Swann told BBC Radio 5 live.
"We need to play in front of full houses, we need to play exciting cricket, but most importantly we just need to win. Three or four wins at the start of this summer and all will be forgotten."
- Sports & Recreation
- Alastair Cook
- Peter Moores
- Kevin Pietersen