You did not experience a contradiction.

The way you perceived a song wandering around with a mustache was by seeing. You did not at the same time actually not see the song wandering around with a mustache. You understood that it wasn't the case, and hence you perceived it not being the case, but saying you perceived something you did not perceive is then totally possible, as long as you perceived something in another sense than the sense in which you did not perceive it. If it was the case that when shifting focus from the mustache-bearing song, you did not see it, then that's further evidence suggesting you did not see something which you didn't see at the same time.

Since you did not experience a contradiction, you have not shown in any way that it is possible for a logical contradiction to be anything but impossible.