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The association yesterday revealed the talented 22-year-old has transferred to Wellington and will play for the Firebirds next season.
The highly-rated right-armer sprang the decision on management earlier this week.
It caught the association off guard and Coggan said the Volts did not have an opportunity to persuade him to stay.
"Firstly it is a shock, secondly it is a big blow," Coggan said.
"And, I suppose, thirdly I’ve know Nathan since he was a 17-year-old coming into our system from Oamaru.
"We always knew he was a big part of our future. And by that I mean we had every plan to build our side around him and a couple of other key players for the next 10 years, so it is a big loss.
"But, at the end of the day, there was nothing we could do about it — he had made his decision.
"He actually contacted Wellington to see if he could progress the move and all we can do really is just wish him well.
"He is a fantastic young man. The day will certainly come, sooner rather than later, when he becomes a Black Cap — it just won’t be from Otago."
Smith indicated former head coach Rob Walter’s decision to transfer to Central Districts played a part in his decision to leave the Volts.
Coggan is confident there will not be any more shock departures. He added there was an agreement among the six associations not to target each other’s players without talking to the affected association first.
That did not occur in Smith’s case because the player made the approach.
"They’ve not had an obligation under the master agreement to contact us and let us know that that conversation was happening. We would have hoped, through goodwill, [Wellington] would have said ‘we are having a conversation with Nathan’.
"We never had that opportunity. Nathan had made up his mind well before we even had an opportunity to talk to him about it.
"So it was a complete surprise on Monday afternoon when I got notified by [a staff member] that he was going to Wellington."