NFA not accepting a certain string
I'll give you a recipe for constructing automata for $\Sigma^* \setminus F$ for any regular $F \subseteq \Sigma^*$.


Construct a (complete) DFA $A_F$ for $F$.
Construct the complement automaton $\overline{A_F}$.
Optional: minimise.


The first step is particularly easy (if maybe time consuming) for finite $F$. The second one is standard (flip accepting and non-accepting states) and should be covered by any textbook on this subject.

Of course, step 1 may blow up the size of the automaton (going from an easy-to-design NFA to DFA); this can in particular be the case for finite sets. In your particular case, though, you never get more than five states.