There is no such feature in Illustrator.
However,
this page
describes an AI Javascript I hacked out for a similar purpose. Take a look at the scripts named JET_SerialNumbers.jsx and JET_NumberedCallouts.jsx.
Alternatively, since you know how to do it a word processor, etc., you can also do it using FillDown in Excel, copy and paste into Illustrator:
1. Open a new Excel file.
2. In the first cell, type "Number 1".
3. In the next cell below, type "Number 2".
4. Select both cells. Drag the Fill Down handle downward as many rows as you want.
5. Select the column. Copy.
6. Switch to Illustrator. Paste. Ungroup.
JET