I was dismissed without warning, is that unjustified dismissal?

Quite possibly. Under the Employment Relations Act 2000, a dismissal must be both substantively justified, meaning there was a genuine reason a fair and reasonable employer could have dismissed for, and procedurally fair, meaning the employer followed a fair process. That usually involves raising concerns, giving you a real chance to respond and improve, and considering your explanation before deciding. Dismissing for poor performance without prior warning or a chance to respond is a red flag. You have 90 days from when the grievance arose to raise a personal grievance with your employer in writing, so act soon. You can ask for mediation through MBIE's free service, and if it is unresolved you can lodge a claim with the Employment Relations Authority. Remedies can include lost wages, compensation for humiliation and possibly reinstatement.