While the complex ICC Test ranking system helped India regain their pole position, Shastri maintained that he will take heart from the fact that the side put up a good show.
Critics and former captains have rounded on the coach, particularly for his mid-series claim that his team is the best to come out of India in 15 years.
Cook, who hit a 71 and 147 in the two innings, described James Anderson, who became Test cricket's highest wicket-taking fast bowler, as England's best player of all time.
Once the 204-run sixth wicket stand between Rahul and Pant ended, India tried to hang on for a respectable draw but it was of no avail.
Rishabh Pant scores maiden hundred as India sniff at improbable victory against England in final Test
The second session certainly belonged to Pant, who hit 14 boundaries and three sixes including one over deep mid-wicket off Adil Rashid to complete a well-deserved hundred.
Indian opener KL Rahul took his overnight 46 to 108 not with some dazzling boundaries to illuminate a murky morning.
By the time Alastair Cook was done, he had also brought up that century 'is 33rd in Test cricket' before ending on 147.
Batting at 96, Cook drove Ravindra Jadeja for a single in the cover region. Bumrah aimed hard at stumps and it resulted in giving five runs to the home opener.
Following a disappointing year, Cook's late flurry has left him with an impressive career average of 45.35.
The day certainly belonged to Cook, who scored his 33rd hundred his last appearance to join a select band of players having scored a hundred on debut and final Test.
Alastair Cook, in his final innings before international retirement, was 46 not out and Joe Root, his successor as England captain, 29 not out.
Ravindra Jadeja top-scored for India with an unbeaten 86-run knock, while debutant Hanuma Vihari contributed 56 before being caught behind off Moeen Ali.
India is touring Australia between November and January next, where they will play four Test matches, three T20s and as many ODIs.
On day one, India reduced to England to 198 for seven, and they finished at 332 on day two, thanks to Jos Buttler's 89.
India lost the ODI as well as Test series to the hosts and the CoA is expected to assess the team's performance after the end of the fifth Test.