Cook, who is set to retire from international cricket, ended the third day of England's fifth Test against India at The Oval on 46 not out.

"He has played really well and has shown everything that he is about," said Farbrace.

"I think he is enjoying milking all the applause he is getting. It's driving him to bat as long as he possibly can."

Opener Cook, playing his 161st Test, made 71 in England's first innings, only his second half-century in 2018.

When he emerged for his 291st and final innings in Test cricket on Sunday afternoon, he was given a prolonged standing ovation by The Oval crowd.

It was a similar story at the end of the day after Cook had guided England to 114-2, a lead of 154 runs.

"He's been pretty calm, but I would imagine that reception when he went out to bat moved him," said Farbrace.

"It certainly moved everyone else in the dressing room."

Cook, 33, will retire as England's most capped Test cricketer, as well as their highest run-scorer, leading century-maker and taker of most catches.

If he manages to complete a 33rd Test century on Monday, it will end a career that began with a hundred against the same opponents on his debut in Nagpur in 2006.

"As much as we will miss his runs and catches, we'll also miss the calming influence that he has amongst everybody," added Farbrace.

"He manages to make everyone feel very welcome. He has the respect of everybody and everyone is comfortable talking to him. He's very down to earth."

England's next assignment is a three-Test tour of Sri Lanka in November.

With Cook not there, it will end his run of 159 consecutive Tests, a record in the longest form of the game.

"Come Sri Lanka, there will be a lot people looking around, realising he's not there and understanding what an impact he has had on the team," said Farbrace.

"He's a very caring bloke. He'll be a huge miss."