India won the third Test against England inside two days after 30 wickets tumbled in five sessions on a turning track in Ahmedabad.
The BCCI said no addition to India's squad will be made for the final Test at Motera.
England on Thursday suffered an embarrassing 10-wicket defeat in the third Test against India on a spin-friendly Motera track to go down 1-2 in the four-match series.
Cook said batting was near impossible on the newly laid strip at the refurbished stadium in Ahmedabad.
The 38-year-old Pathan was part of the inaugural T20 World Cup-winning side in 2007 and also the one that triumphed in the 2011 ODI World Cup at home.
Hayden, who scored 8,625 runs in 103 Tests, also had a piece of advice for the England batters, who have struggled against the likes of R Ashwin and Axar Patel.
Spinners claimed 28 of the 30 wickets that fell in five sessions in the shortest completed Test match since 1935.
Ashwin became the fourth Indian to take 400 Test wickets when he dismissed Jofra Archer on the second day of the day-night third Test.
The hosts need a draw in the final Test, also in Ahmedabad from March 4, to reach the WTC final against New Zealand.
TV umpire C Shamshuddin oversaw several close calls on a frantic 13-wicket day which ended with India gaining the upper hand.