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Both Anderson and Jadeja were cleared of breaching the ICC Code of Conduct following the incident at Trent Bridge, although Dhoni says that Anderson should have punished for verbal abuse.
Speaking at a press conference ahead of the fourth Test at Old Trafford, Dhoni began by lamenting that charges could not be upheld against Anderson due to a lack of evidence.
"Well I think in our society, there is something called evidence. And lack of evidence is also something," he said.
"What we are really talking about - it is mostly along those lines. But surely now, it is time for us to move ahead."
However, when pressed about the situation, Dhoni says, in no uncertain terms that he thinks Anderson's behaviour was unacceptable.
"If somebody is very consistent with the abuse, then definitely he should be punished.
"Doesn't matter who he is. Once the umpire goes and tells him like 'we have really had enough' and foul language should not be used on the field, that is the point where the individual doesn't curb his instinct, he needs to be punished.
"But it has shifted a lot the way that cricket is played, it is constantly on the move, so I think we will have to be careful as to where we are going," he added.
Reflecting on the way that the incident has come to overshadow the five-match series, which is level at 1-1, Dhoni maintains that his team were completely in the right to bring charges against Anderson.
"We brought forward something that we thought was unacceptable when it comes to the game of cricket.
"And beyond that, it is not in my jurisdiction to award penalties or punishments.
"I mean, what we thought was bad for the game of cricket we brought it forward.
"It is up to the ICC and others to decide what really gets done; it is nothing between me and Jimmy Anderson that, you know."
Video courtesy of SNTV
© Cricket World 2014