Cook described the reported altercation between Anderson and Jadeja at Trent Bridge, and the tourists' response to it, as a case of making a "mountain out of a molehill".
India elevated their allegations against Anderson, "pushing and abusing" Jadeja as the pair made their way through the narrow lobby of the pavilion for lunch on day two of the first Test, to Level 3.
That implies a seriousness commensurate to a much heavier penalty scale than those prescribed for more Level 1 or even 2 offences.
The potential punishment for a player found guilty of a Level 3 offence, under the International Cricket Council's code of conduct, extends to a four-Test suspension.
Only three Level 3 charges have previously been made, although Level 4 also exists.
The England and Wales Cricket Board responded immediately by describing last week's incident as "minor", and Cook confirmed at his press conference on the eve of today's second Test at Lord's that a counter-allegation against Jadeja is on its way to the ICC.
Receipt of that has yet to be confirmed by the world governing body, but it is understood ECB has sent a Level 2 charge to Dubai.
Cook was unequivocal when asked if India's motivation might be to try to eliminate Anderson for latter stages of the five-match series, which stands at 0-0 after the Nottingham stalemate. "I think so. I think that's pretty much where it's come from," he said. "It's probably a tactic from India, if we're being honest."
Anderson and Jadeja's disagreement began after the latter was given not out to the seamer, and continued as the teams made their way off for lunch. There have been suggestions that India might have become poorly disposed towards Anderson previously and made the charge on that basis, rather than merely because of what did or did not take place in the stairwell.
Cook said: "I think it should be on that one incident . . . they should make sure it's that. In my opinion, it's a big mountain out of a molehill . . . We're surprised it's come to the situation it has come to."
Cook must ensure that the controversy does not put his team off their game as they try to arrest a run of nine Tests without victory, their worst Test sequence for more than 20 years. "We just can't let this be a distraction for us as a side," he said.
"We can't sit here in five days' time, and [be talking about] the build-up to it. There's been toing and froing between Jimmy, Peter Moores [England's coach] and the hierarchy at the ECB as well . . . and there has been a charge levelled back at Jadeja. I think that's quite obviously reasonable."
Cook declined to discuss the specifics of the incident, because he is not allowed to do so. However, he did appear to momentarily forget that protocol when he added: "We're just surprised it's a Level 3 incident, after hearing they've started it - certainly after hearing what happened." A hearing before a judicial commissioner, within 14 days but with the possibility of further delay in extenuating circumstances, is the established ICC procedure for a Level 3 incident.
Anderson is therefore almost certain to be free to play at Lord's, and probably in next week's third Test in Southampton, but will surely have extra unhelpful matters on his mind at both venues.
"For Jimmy, all the lads will rally round him," said Cook. "He's a stalwart of our side, an outstanding bowler with a fantastic record."
Cook is optimistic, too, that he and Dhoni, Jadeja's batting partner at the time of the Trent Bridge fracas, will have the authority to ensure relations between their teams do not descend irrevocably this summer.
"I hope not," he said. "MS and I have that responsibility as captains of the side to make sure we control our players, and do not let that happen. We have a responsibility to people watching the game, responsibility under the ICC rules."
Dhoni, however, was unrepentant about India's decision to make an allegation of Level 3 seriousness against Anderson, "We felt what happened was wrong, so we went ahead with the charges," said the captain, who was also adamant that the allegation was not tactical.
"It's not something we have done ... let's realise the facts," said the India captain. "You can put it in whatever way possible, but there are certain things that need to be followed and should be followed."
Dhoni also congratulated Jadeja for his restraint. He said: "I think it was good on Jadeja not to really do something. It could have gone a bit far, but I felt he addressed it in the most appropriate manner. That's something we will have to learn and move forward. Somebody has to back off at the right time. We play a sport and a lot of people look up to us."