Anderson experienced soreness in his ankles and shoulder during the previous test in Mumbai, prompting team management to withdraw him from what is essentially a contest of academic interest following India's unassailable 3-0 lead.
"It's not worth the risk," Cook said of the 34-year-old right-arm paceman. "When he has been in this situation over the last six months and we have played him, he has picked up injuries.
"It doesn't seem the right time to play him."
Anderson returned from a shoulder injury to play the second test against India, taking four wickets in his team's defeat at Visakhapatnam.
He went wicketless in the subsequent tests in Mohali and Mumbai as India sealed the series with a match to spare.
The decision to mothball Anderson was also a clear indication that his team expect the ageing bowler to play a key role in the next summer.
"I'm very confident he can make a big contribution to English cricket over the next couple of years," Cook said. "But we're going to have to manage him a bit more in tests. He might miss a couple more tests as a precaution, he might not.
"With a couple of months off now, his body might fly again. He's a very athletic guy and he's very light on his feet. He can still make a big difference to English cricket over the next couple of years."
A decision on the availability of fellow paceman Stuart Broad, returning from a foot injury, would be taken after Thursday's practise, Cook added.
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
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