For an NFA with ε-moves (also called an ε-NFA), the construction must be modified to deal with these by computing the ε-closure of states: the set of all states reachable from some given state using only ε-moves.
During the powerset computation, compute the ε-closure \{q' ~|~ q \to^{*}_\varepsilon q' \} of each state that is considered by the algorithm (and cache the result).