Sky Blues' chief executive Tim Fisher has accused the former Manchester United striker of leaving the club in the lurch following his five-month tenure.
"To say we are disappointed is an understatement,' he said. 'We gave Mark a three-year contract which we saw as a long-term appointment.
"Added to this, Mark was able to bring in those members of staff that he requested, plus we gave a considerable financial commitment in terms of players brought in during the loan windows to ensure that we had a strong, competitive team on the pitch.
"Over the last few months, we have had several clubs interested in securing Mark's services and we have fought off multiple approaches. We made every effort to ensure he stayed with us.
"Once it became obvious that there was no way forward we had no choice but to eventually allow him to speak to Huddersfield."