Performance of CNG in comparison to Petrol is always less. I don't own a vitz but my Corolla 80 (1300 cc) non-EFI runs very well on CNG as well.
Vitz is a 1000 cc but it has an EFI engine. I don't think it would be such a big deal running it on CNG.
I would still suggest that you run it by someone who owns a Vitz with Auto Transmission and is running it on CNG. He would be in a far better position on advisin than me.
Anyways whatever you find out please share it here as well.
Take Care and Best of Luck