I think this could fail under certain test cases, however.

class Solution:
    def minExtraChar(self, s, dictionary):
        # build the Trie
        root = TrieNode()
        for word in dictionary:
            node = root
            for ch in word:
                if ch not in node.children:
                    node.children[ch] = TrieNode()
                node = node.children[ch]
            node.isEnd = True

        # iterate over string counting unused characters
        totalUnused = 0
        curUnused = 0
        node = root
        for ch in s:
            curUnused += 1
            if ch not in node.children:
                totalUnused += curUnused
                curUnused = 0
                node = root
                continue
            node = node.children[ch]
            if node.isEnd:
                curUnused = 0
                node = root
        totalUnused += curUnused
        return totalUnused