The definition does not include items which should be included.
This fallacy is made when the definition clearly does not include items that should be included. This fallacy can be committed at the same time as a too broad fallacy, if the definition also includes items that should not be included.
An apple is something which is red and round.
Golden Delicious apples are apples, however, they are not red (they are yellow). Thus they are not included in the definition, however, they should be. Since Mars is also red and round, this definition is also too broad.
A book is pornographic if and only if it contains pictures of naked people.
The books written by the Marquis de Sade do not contain pictures. However, they are widely regarded as pornographic. Thus, the definition is too narrow.
Something is music if and only if it is played on a piano.
A drum solo cannot be played on a piano, yet it is still considered music.
Identify the term being defined. Identify the conditions in the definition. Find an item which is an instance of the term but does not meet the conditions.