Let's be careful about wording. You say that (1) time doesn't exist. You also say that (2) time is a concept that was invented by humans. If time is a concept, then I don't know which concept it could be except the concept of time. But if time is the concept of time, then each of them is the concept of a concept of a concept (and so on without end), which is an unintelligible regress.
Even if time isn't the concept of time, your assertions (1) and (2) are inconsistent with each other. If time is a concept that we succeeded in inventing, then our invention must exist (or have existed), in which case (1) is false. You asked for a refutation of the statement that time is not real but merely a concept. Unless concepts aren't real, there's your refutation.
So I take it that you mean, instead, that (3) the concept of time is an unfulfilled concept, like the concept of a unicorn: nothing answers to the concept, even if the concept itself exists. In that case, I haven't answered the question you meant to ask: Why think that time exists, i.e., that something does indeed answer to our concept of time? I don't have a good philosophical answer to that question, but I'd point out that the equations in our best physical theories require time as a parameter. In any case, I hope that what I've said is helpful in at least sorting out the question.