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The Welsh club said it had been unable to secure a licence for 2027, despite believing it had met every requirement set out by the Rugby Football League (RFL).
It said it had provided financial assurances from three separate parties and completed every fixture during the 2026 season.
The decision affects Cumbrian clubs and their league.
According to the statement, the central issue concerns proposed escrow arrangements and the conditions attached to them.
North Wales Crusaders said: "It is with deep regret that we have not been able to secure a licence to compete in 2027."
The club said it believed any escrow arrangement should be "fully independent, without unreasonable rules or restrictions imposed upon it".
It added: "We are incredibly saddened by the position we now find ourselves in. However, we cannot agree to the RFL's current stance on these terms."
Competition arrangements for both clubs remain unclear.
Despite this, Crusaders said their commitment to rugby league in Wales remained unchanged and they would be ready if the RFL reconsidered.
North Wales Crusaders said: "Should the RFL reconsider its position and grant us a licence, we stand ready to compete in 2027."
The statement thanked supporters, volunteers, board members and staff. It described the decision as "This is a deeply disappointing setback, but it is not the end of our journey."
If a return for 2027 is not possible, the club said it would continue building towards 2028 and beyond.