Anderson was accused of misbehavior after the incident during the drawn first Test.
Cook also remarked that they could not let India's tactic be any distraction for their team.
Jadeja was also charged under the International Cricket Council's (ICC) code of conduct.
The England and Wales Cricket Board had sent a level two counter-accusation against Jadeja to the ICC.
A level two allegation puts a fine of 50-100 percent of the player's fee for the match and/or a possible ban of two one-day internationals or one Test.
Cook also said in a statement that India was trying to get Anderson banned, reports the BBC.
Indian captain Mahendra Singh Dhoni denied that it had been a tactic against Anderson.