Carter, who succeeded Andrew Glover a fortnight ago, sold Australian scrum-half Tim Smith to Salford at the weekend to pay the players' wage bill for August but says the club still has a shortfall of around £400,000.
The 44-year-old businessman told a news conference at the Rapid Solicitors Stadium that the club is not close to going back into administration and gave an assurance that it would still be in Super League in 2014.
"This club will carry on," said Carter, who is now running the club with fellow director Chris Brereton, with chief executive James Elston becoming chief operating officer.
"I've put a lot of money in and Chris has put some money in but we are not rich people, we are fans.
"We've got a budget in place for next season which we think we can live with. If we can get to the starting point, I think we can get through this as a competitive Super League team but we have issues to deal with.
"This club has spent more than its earned so we're in a hole. It's not rocket science, we have got to cut our cloth accordingly
"If we got £400,000 we would be good to go. If we don't get that, then we will have to sell players."
Carter, who is thought to have received around £90,000 for Smith, rejected a similar offer for club captain Danny Kirmond but says the club have received four offers for prop forward Kyle Amor.
"Tim Smith went because I needed to pay wages," he said. "At the same time I got a decent offer for Danny Kirmond but I didn't have to sell.
"But, if we don't get investment in the next couple of months, players will have to be sold.
"And anybody who tries it on will get short shrift. We know the value of a player and nobody is getting a cheap deal out of Wakefield.
"I hope the sale of Tim Smith is the end of it but I can't promise it."
Glover took the club out of administration on the eve of the 2012 season but, according to Carter, they have led a "hand-to-mouth" existence and recently fought off seven county court orders.
Carter says he has agreed to buy the shares of Glover, who will stay on at the club to oversee the proposed move to a new ground at Newmarket and has the backing of head coach Richard Agar.
"Andrew has given me a complete undertaking that he will not pull any of his money out," Carter added.
"We've undergone a total restructuring and basically me and Chris are running the shop. We're full-time at the minute but neither of us have taken a penny out of this club and we're not expecting to.
"We've talked to Richard and he's up for the fight. It will be difficult but we're not afraid of hard work. If we have to put in 60 hours a week, we will."
Carter accepts that Agar will inevitably be forced to operate on a shoestring budget for 2014, at the end of which two clubs will be relegated from Super League.
"We will still have a club next season," he said. "We are trying to put the club on a sound financial footing without a benefactor. We will always strive to be a part of Super League but, if we go down, we would want to come straight back up."
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- Super League