No, you don't understand: the conclusion of the Chinese room argument is precisely your statement "more stuff inside is needed for understanding it, than just input and output." That's precisely why consciousness is not a reduction to executing the proper computer program.

Maybe you're not clear on what computers are? I strongly encourage you to look up for example the definition of Turing machines. They do not have any "stuff inside"; they consist of a subset of mathematical functions from bitstrings to bitstrings,

    data NextMove s v = GoLeft s v | GoRight s v | Halt v
    newtype TuringMachine s v = TuringMachine (s -> v -> NextMove s v)

A Turing machine is a mathematical function, a subset of (s, [v]) -> [v] that can be generated by the above functions.

Mathematical functions are defined as pairs of inputs and outputs. There literally is no "stuff inside" them. They're just sets of (input, output) pairs satisfying left-uniqueness: if (i1, o1) and (i1, o2) are both in the function then o1 = o2 and they were the same pair all along.

Again, Searle is happy that our brains are computers and happy that our brains are conscious. But they are not conscious by virtue of running the right computer program with their computational aspects. In fact, getting you to compute something is relatively hard and unnatural, which is why computers are so great as calculators whereas it takes many years to teach humans the same.