"There were was no backbone shown by India," Gavaskar told a leading British channel.
"They (Indian players) showed no determination, the dismissals were soft, there were no great deliveries, England were just persistent," said Gavaskar, one of cricket's greatest opening batsmen.
"You could see Indian heads go down and thereafter there has been no thinking of 'let's fight," he added.
Former India wicketkeeper Engineer was also equally critical of the players, saying that they played without "passion" and showed not guts to fight.
He also criticised "highly paid" coach Duncan Fletcher for not advising captain Mahendra Singh Dhoni to field first after winning the toss.
India lost the Test by an innings and 54 runs to trail the five-match series 1-2.
"This was embarrassing. India shot themselves in the foot right from the moment they decided to bat on a green top surface," the 76-year-old Engineer, who played 46 Tests from 1961-1975, told a British radio channel.
"There was no backbone shown by India. They played without any care or passion, like having a Saturday afternoon slog," added Engineer.
He said Fletcher, a former England coach, ought to have told Dhoni to field first, rather than bat.
"Fletcher is very, very highly paid, surely he can read the pitch and advise Dhoni accordingly?" questioned Engineer.
After Dhoni won the toss and batted, India collapsed to eight for four inside six overs. They then lost nine second-innings wickets after tea on Saturday as England won with more than two days to spare to go 2-1 up in the five-Test series ahead of next week's finale at The Oval.
It was the first time England had won a Test against India inside three days since a 132-run victory at Birmingham's Edgbaston ground back in 1967.

"There is only a bit of pride to play for because they've been humiliated. I dare not see the papers in India, they must be so critical, and rightly so," Engineer said.
Asked about the poor performance of highly-rated Virat Kohli, who has scored only 108 runs in the series at an average of 13.5, Engineer said, "Virat Kohli came here with a great reputation and has just not taken off, he has been out to silly deliveries."
Engineer was also critical of the BCCI'S ongoing opposition to the use of Decision Review System in matches involving India.
"The DRS is absolutely haunting India because a lot of the decisions have gone against them. I don't know when they'll open their eyes and wake up. They've got to embrace
DRS," Engineer said.
"The ICC (International Cricket Council) are just not firm enough, can they not put pressure on India? All the other countries have agreed to it, why can't you?" he further said.

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