Carter took over at the helm of the Super League club earlier this month and said in a statement released on Saturday morning that the Wildcats were "under-capitalised to the tune of somewhere in the region of £400,000".
As a result of that, Carter says he has sold Smith, one of coach Richard Agar's key players, to Salford for a "substantial fee", although the ambitious Reds have not confirmed the move themselves.
Carter did add, though, that he had turned down a six-figure offer for captain Danny Kirmond, which should at least offset the blow of Smith's departure.
Kirmond recently signed a new contract and Carter said two more players had followed suit, adding: "On the positive side, we have managed to extend the contracts of some of our key players. I have already mentioned Danny, but also Dean Collis and most recently Lee Smith and Ali Lauitiiti have all signed up for next season."
Wakefield have been in financial trouble before and were bought by current owner Andrew Glover while in administration at the start of 2011.
Earlier this month Glover stepped down as chairman after seeing off nine county court judgements relating to the club's finances.
Saturday's announcement suggests they still have problems to face, however.
"It's no secret that the vast majority of Super League clubs all need significant investment and this is usually financed by wealthy owners. Wakefield doesn't have one of these, so to be a success we need the people and businesses of Wakefield to come forward," Carter said, before touching on the club's plans to move to a new ground in the Newmarket area of the city.
"I know with a lot of hard work and a little luck, we can get this club to Newmarket as a Super League club. It is more important than ever that you stick with me and my small team to manage this business properly. Should there be anything of great magnitude I will endeavour to tell you all as soon as I possibly can.
"The question remains, does this great city of Wakefield want a full-time professional Super League club, or not? If the answer is yes, then I need your support more than ever before."
If Smith is now a Salford player, his arrival kicks off a week of announcements at the club.
Owner Dr Marwan Koukash has called a special event for both fans and the media on Thursday, where Castleford's former Man of Steel Rangi Chase is expected to be unveiled as one of a number of new signings.