Hi Salik and welcome to the forum.
Have you looked into applying for a
Working Holiday Visa ? It depends which country you are from whether there is a scheme running or not. Unfortunately it wouldn't be for 3 years but, for some countries, it can be up to 2 years. You don't need a job offer and you don't need any particular skills to apply so it's the easiest way in.
If you had skills that NZ wants you could have applied for a
Work Permit which you can get for up to 3 years, with the option of extending. If you are an administrative manager you could probably have scraped in.
It really is quite difficult to get into NZ long term unless you have what they want or you have someone to sponsor you.