The loss in Mohali, which gave India a 2-0 lead in the five-match series, was England's fifth Test in six weeks.
With the next Test in Mumbai not beginning until 8 December, a number of the England squad will leave India for a holiday in Dubai.
"We will get away, see some different scenery and come back for the last two Tests," Cook told BBC Sport.
England's two-Test series in Bangladesh, which was drawn 1-1, began on 20 October.
They then travelled straight to India where, after a draw in the first Test, Cook's men have suffered two heavy defeats.
"I think most people would agree that five back-to-back Tests in six weeks is a heavy schedule," added opener Cook, who has spent just 18 hours with his daughter since she was born midway through the tour of Bangladesh.
"I genuinely believe if we put a better standard of performance in we can put India under pressure, we just haven't done it yet."
By the end of their tour to India, England will have played seven Tests in two months and 17 in total in a 2016 that also included a run to the final of the World Twenty20 in March and April.
Their congested schedule is part of a modern trend that sees tours packed with international matches, while also including fewer rest days or warm-up games.
England coach Trevor Bayliss said: "It's been a long tour.
"The break will give the guys time to get away, refresh mentally and physically and come back ready and raring to go.
"These tours are what you've got to put up with these days. A lot of the teams are going through the same thing and a lot of the players and staff are saying the same thing - it's becoming too much."
Former England captain Michael Vaughan on Test Match Special
Mentally it's going to be a challenge. When you're 2-0 down and you can only draw, it's always a challenge.
The one thing in their advantage - the one thing they can grab at - is they're playing the fourth Test in Mumbai. The last two times they've been there, England have won the Test.
England's players need a break after the third Test defeat by India, according to captain Alastair Cook.