So as you see from the others what you are asking for doesn't exist in Vi (AFAIK).
Undo undoes what your last action was. If your last action was to enter insert mode and then add a line and then exit insert mode. That will be undone, however if from the default mode you hit the "x" key then you will delete 1 character or if in visual mode with text selected the text will be deleted. If you hit undo then you will restore that one character or the text that was selected.
...You should think of this as an action, and actions can be atomically undone or restored
As mentioned previously if you wish to delete the previous word then you should be able to hit Ctrl + w and delete the previous word while remaining in insert mode.
If you exit insert mode you can navigate (motion) back a word with "b" forward a word with "w" to the end of a word with "e", and can cut (which leaves you in insert mode) with "c" or delete with "d". Both actions cut and delete can accept a motion following them so you can delete the current word / up to the next word with "dw" or cut the previous word with "cb"
This concept becomes more useful when you remember to use the "." command (in normal mode). This command is to repeat the last action. I have used this many times to find and replace a small group of words in a file (It is especially useful if you are paranoid about changing too much). The scenario would be the following:
File:
This is my post
really it is a test
this is the middle
This is the end
if I wanted to replace "is" with "was" I could write:
%s/\<is\>/was/g
however if I wanted to change the first line and the third line "is" to "was" (and I didn't know their line numbers, and I wanted to see if there were any other places I wanted to change is to was I could type
"/is"
hit "n" until I reach the place I want substituted, and then hit "cw" and type "was"
I can now hit "n" until I reach another place I want substituted and hit ".", and that will replace "is" with "was" (Note: my search string didn't limit to the word "is", just the two characters "is" so "This" & "this" will match in this case)