Carr has come under heavy criticism for his management style and for reportedly influencing Martin in to making the negotiation process difficult.
"I stand by everything I have said and I stand by the way I have represented this kid. My business has been sullied and my reputation has been damaged," Carr told Fairfax Media.
"I care about Dustin. He's a terrific kid and I've been misrepresented. I'm not an advocate for players changing clubs and I've always hoped that Dustin would stay at Richmond. He wears Royce Hart's number for heaven's sake.
"I've told Dustin that, just as I told Travis Cloke that last year. Richmond knows our position and there needs to be some dialogue."
The 22-year-old reportedly missed a key meeting with Tigers football manager Dan Richardson and list analyst Blair Hartley.
Martin has asked the Tigers to deal with his management, while the two parties are yet to meet this week.
Richmond's contract offer is nearly $1 million over two years – but with specific behavioural and performance based clauses.
No club is yet to make a formal offer to Martin and his management and Richmond have repeatedly declared he is a required player.
If left unsigned Martin could become available via the draft.