The tourists started off with a strong performance in the first drawn Test in Rajkot.
The tourists, who lost the series 3-0 trail after the fourth Test loss in Mumbai, started off with a strong performance in the first drawn Test in Rajkot but could not keep pace with top-ranked India.
Cook's role as a leader has been brought into question after the three consecutive defeats but he insisted that it is all part of the job.
"You get judged on your results as a captain don't you? And when you lose games of cricket you are under fire, it happens to everyone," Cook said.
"When Virat (Kohli) loses games of cricket he'll get criticised, when I lose games of cricket I get criticised. That's part and parcel of the job.
"Look at Dylan Hartley the England rugby captain. He wins games of rugby and it's all flying and obviously an incident last week (when he hit an opponent in the face) he gets criticised," added Cook.
Cook admitted reading the pitch wrong in the Mohali Test and also regretted using just two spinners in Mumbai.
"When you're part of the leadership group you live and die by those decisions and when it's going well everybody thinks you're brilliant and when you're doing badly everybody thinks you're terrible," he said.
Cook insisted England's effort could not be criticised as they search for a consolation win.
"We've put everything into this tour. I'll have no regrets on the effort and clearly we'd rather not be 3-0 down.
"One thing you can't fault us on is how hard we've fought as a side and I'm proud of how we've stuck together," Cook told reporters.
Cook, who has said that Joe Root is "ready" for the captain's job, was again asked about his likely successor.
"The moment he got off the plane in India in 2012 as a very young-looking Joe Root you knew he was ready for international cricket - you knew.
"Everything you knew -- his mind, his game -- was ready. Every challenge that's been thrown at him he's handled. So I don't think anything over the next few years will faze him," said Cook.
England and India had a light training session after two days of no practice as the ground staff at Chennai's M.A. Chidambaram stadium worked overtime to ensure the pitch and the outfield are ready for Friday's start.
The city is recovering from devastation caused by Cyclone Vardah that hit on Monday.
"This will be my 140th game and I've never played in a game when we haven't had nets before. But we've had a lot of cricket and sometimes you do have to remember what happened in the cyclone, when people unfortunately lost their lives.
"So a net session the day before doesn't seem quite as important after what people have gone through. Driving around you can see the devastation and it's a real reminder of how lucky we are," said Cook.