"Jimmy is an outstanding bowler with a fantastic record. It’s probably a tactic by India, if we are being honest," Cook told reporters.
Asked if India would rather have Anderson out of the England team than in it, Cook said: “Yeah, I think so, I think that’s pretty much where it’s come from."
Cook, who admitted he did not see the incident, said England were surprised Anderson was charged with a level-three complaint, which is the most serious offence under the ICC code of conduct.
If proved it could lead to a ban of up to four tests.
"We are a bit surprised it's a level three (offence), to be honest. It's a bit of a mountain out of a molehill," added the captain.
"For Jimmy, all the lads are rallying round him. He is a stalwart of our side. He is an outstanding bowler with a fantastic record.
"We can't let this be a distraction ... but at certain times in this test match Jimmy will let his bowling do the talking."
Cook said he would not be telling Anderson to tone down his natural aggression during the test.
"He is a very competitive guy. Jimmy is up for the game and desperate to do well for England."
England have made a counter-claim to the ICC against Jadeja but Cook said he hoped the row would not sour relations between the two sides.
"Both (Indian skipper) MS Dhoni and I have a responsibility to control our players, a responsibility to the people watching the game and to the ICC," said Cook.
Dhoni, whose news conference followed Cook's, said: "We felt what happened was wrong, so we went ahead with the charges. We felt Anderson overstepped the mark and crossed the line.
“We talk a lot about the spirit of the game and everything, and the guidelines that need to be followed. There have been a few individuals from our side also in the past who have crossed that line and it’s a very difficult one.
“You can be aggressive, you can be vocal, and it’s fine. But there are certain guidelines that are laid and we should be following all of them," he said.
Former India test captain Rahul Dravid, a television pundit for the series, denied India's motive was tactical.
"I don't think India would stoop that low to get Jimmy Anderson suspended," he told Sky Sports.
Following criticism of the Trent Bridge pitch for the opening match of the five-test series, Cook said the Lord's wicket looked good.
"There is a covering of grass but Lord's wickets are noted as being good wickets," said Cook. "But because it is not an exact science we will not know (how good it is) until tomorrow. We shall have to wait and see."
The Trent Bridge draw was England's ninth test without a win, and another draw or a defeat against India this week would equal a winless streak stretching back to 1992/93.
(Reporting By Tony Goodson, editing Pritha Sarkar)
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