Cotchin was reported during the Tigers’ big loss at the MCG on Sunday.
In reviewing the incident, the match review panel found the contact was high on the body, of a high impact and was reckless.
It meant the incident became a level four offence, attracting a four-game suspension.
Cotchin could have had the penalty reduced to three weeks by lodging an early guilty plea.
But he has decided to contest it as he and the Tigers believe the suspension was too harsh and should be reduced.
Speaking on Monday night on One HD’s One Week At A Time program, Cotchin hinted he was disappointed with the MRP’s finding.
But he admitted his actions in collecting Wright were unwarranted.
“I’m obviously very disappointed with myself because I let the team down,” Cotchin said.
“I probably needed to put the hand out to spoil, which would’ve made it not look as bad as it was.”
All the other players cited by the match review panel have accepted their sanctions, which means Port Adelaide’s Daniel Motlop will miss the next two games, while Brisbane Lions defender Ashley McGrath won’t play in his team’s clash with Geelong at Skilled Stadium on Saturday.
Motlop was suspended for rough play against Bulldog Shaun Higgins, and McGrath copped a one-game ban for rough play against Hawthorn skipper Sam Mitchell.
Carlton’s Andrew Walker has accepted a reprimand and 70.31 points towards his future record for bumping or making forceful contact from front-on against Sydney Swan Ben McGlynn.
Adelaide veteran Michael Doughty, North Melbourne’s Michael Firrito and West Coast’s Eric McKenzie have also taken reprimands for striking and rough play offences.
Brisbane Lions youngster Jack Redden, Melbourne’s Jordie McKenzie and West Coast midfielder Andrew Embley have all accepted fines for making negligent contact with an umpire.