Cook, unofficial vice-captain on the Caribbean Test tour, was the first man dismissed in the capitulation to 51 all out on Saturday afternoon - when the tourists lost by an innings.
Calls for change followed. But England have only Owais Shah in reserve as batting cover, a fact which may suggest to some players are too comfortable in their positions.
The same batting unit collapsed in Adelaide during the 2006-07 Ashes to 'gift' Australia victory, and were dismissed for just 81 against Sri Lanka in Galle last winter.
"Everyone realises what playing for England means, and there are a lot of good players coming up," said Cook.
"If you don't perform then you know what is going to happen.
"But it is not a time for rushed decisions. There are some very good players, some great players in our side, and things like this have happened before in cricket.
"We cannot act too hastily. The players involved are ultimately responsible, but we have got to take it on the chin and hope we can get a fresh start when we get to Antigua (for the second Test).
"If it happens again, then things have to change. But those are three isolated incidents over three years, so it is not as though it is happening every week."
In the absence of a head coach, following the sacking of Peter Moores, captain Andrew Strauss has urged his players to take personal responsibility for their performances - and that has meant nowhere to hide for the XI bowled out in little more than two hours.
"When things go like that we have to hold our hands up and say 'that wasn't good enough'," Cook admitted.
"We are not reinventing the wheel - that is always the way it has been.
"When there is a focal point like a head coach then maybe responsibility gets shifted on to other people, but here the players must take full responsibility."
Cook dismissed suggestions that the team became distracted by the Indian Premier League auction midway through the Test as "an absolute load of rubbish".
"When you're out there in the middle you're not focused on anything else that's happening," he said.
"But momentum is such a strange thing.
"We were just behind the eight ball after the first innings, with them having a lead of 70-odd, and I have never experienced that happening before.
"It has obviously happened before in other sides, but we hope it won't happen again.
"The one thing we must do is stay together as a side.
"You have to retain your self-belief as individual players.
"You go through lots of ups and downs. But ultimately if you don't believe in yourself out there you will not score runs or take wickets.
"Believing is the one thing that keeps you going in the tough times."
On a personal level, the past 12 months have been a tough time for Cook - who has failed to build on an extraordinary start to his international career.
Cook's seven Test hundreds before his 23rd birthday was previously bettered by only Sir Donald Bradman and Sachin Tendulkar at the same age. But he has not managed one since the final Test in Sri Lanka in December 2007.
"It is a monkey I would like to get rid of as soon as I can," said Cook.
"I honestly can't think of one little thing - form in terms of every player fluctuates, and it is how you come out the other end - but it is down to me to try to change that.
"There is no better feeling than scoring Test hundreds; if you could do it every day you would."
West Indies, meanwhile, will make at least one change to their winning line-up from Kingston.
Xavier Marshall paid the price for his second-ball duck and has been axed from the 14-man squad - so new call-ups Lendl Simmons, who hit a brilliant 282 against England for West Indies A, and Ryan Hinds are vying to replace him on Friday for the second Test.
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team steve, droylsden (10/02/2009 at 12:34)
dessie, manchester (10/02/2009 at 14:48)
yeah a sunfilled holiday sat on a beach and a day stood around the pavillion chilling out!!! what a life?????