saying `I was not a little upset' when you mean `I was very upset' is an example of litotes.
Examples of litotes
litotes
Japanese employs litotes to phrase ideas in a more indirect and polite manner.
From the en.wikipedia.org
It was litotes that gave the speakeasy bars of Prohibition America their outer mystery and inner charm.
From the independent.co.uk
Mandarin Chinese also employs litotes in a like manner.
From the en.wikipedia.org
I suspect, because of the litotes you used.
From the economist.com
It makes the rhetorical figure of litotes ambiguous.
From the en.wikipedia.org
The rhetorical term for this is litotes.
From the en.wikipedia.org
The use of litotes appeals specifically to certain cultures including the northern Europeans and is popular in English, Russian, and French.
From the en.wikipedia.org
More examples
Understatement for rhetorical effect (especially when expressing an affirmative by negating its contrary); "saying `I was not a little upset' when you mean `I was very upset' is an example of litotes"
In rhetoric, litotes are figures of speech in which a certain statement is expressed by denying its opposite. For example, rather than merely saying that something is attractive (or even very attractive), one might say it is "not unattractive".
A figure of speech in which the speaker emphasizes the magnitude of a statement by denying its opposite; a figure of speech in which understatement is used with negation to express a positive attribute; a form of irony
(litote) An instance of litotes
Understatement by negating the opposite; a type of meiosis. "I was not disappointed with the news." See also: meiosis.
(pronounced lee-TOE-tays): A form of meiosis using a negative statement. (See more under discussion of meiosis.)
The opposite of a hyperbole where the significance of something is understated.
Use of understatement affirming something by means of the negative of its opposite; e.g., Hebrews 4:15 For we do not have a high priest who is unable to sympathize with our weaknesses, but we have one who in every respect has been tested as we are, yet without sin. (NRSV). Pronounced "LI-te-teez."
This is when you understate an idea in order to convey the opposite idea. This is normally done through the use of a negative negative before one of the words in order to express a strong affirmative. This style is evident in Karen Hess's Out of the Dust.