"Cook is feeling that a score is close, and you saw that he fought and scrapped and worked as hard as he possibly could. There is absolutely no question that he is our leader," Farbrace said.
A struggling Cook made 22 before being caught behind off Ishant Sharma as the Three Lions were struggling at 105 for four in a chase of 319 runs for victory on day four of the second Test.
England's top-order has been a cause of concern as Cook, Ian Bell and Sam Robson are struggling to get big runs while Joe Root and Moeen Ali are fighting hard to provide England hope.
"You've got to turn up expecting your batsmen to score the runs," said Farbrace.
"We've got somebody at the crease who batted all day at Headingley two Test matches ago, and got a hundred, against all the odds."
"There were a lot of people that day not expecting us to still be at the crease at seven o'clock, and fighting for our lives. Unfortunately, the penultimate ball finished the game.
But it was a magnificent fight. But it's up to us to show the fight tomorrow that we showed at Headingley," he added.
Murali Vijay scored 95 runs and then Ravindra Jadeja scored his maiden Test fifty and added 99 runs with Bhuvneshwar Kumar in a whirlwind partnership that nearly knocked out England. He returned to take the wicket of Sam Robson as well and will play an important role on day five.
"There is no question that Jadeja's innings has given them a big advantage. But we've got two people at the crease who enjoy a scrap. They bat well together. Moeen was talking about playing Jadeja off the rough and if they can give us a good partnership in the morning, we've got people who can come in and strike the ball cleanly," said Farbrace.
"You've got to expect to win a game - that's the key. We're desperate to win this Test match, and we do have an opportunity. It is definitely going to be tough because we are slightly up against it," he added.