Do I have to add " just" in this example?

If I say : " my hair is still wet because I have washed it", is it clear that the washing of the hair was a recent event or do I have to add " just"? To me the fact that the hair is still wet makes it clear that I washed it only a short while ago. Someone told me if I don't add " just", it could mean I washed my hair at some indefinite time in the past. I find this very strange, because like I said before, the fact that the hair is still wet is prove of recent action. What do you think?