The bowler is alleged to have abused and pushed Jadeja "immediately after they left the field for lunch on Thursday".
However, the England and Wales Cricket Board have given their full backing to Anderson in wake of the allegations.
"It's probably a tactic by India, if we are being honest," Cook told reporters ahead of the second Test at Lord's. "Jimmy is an outstanding bowler with a fantastic record.
"We will just rally behind him and hopefully we will get the ball swinging at a certain time in this Test match."
England and India play the opening day of their second Test at Lord's on Thursday.