Apologizing to your little brother will teach him more than any lecture ever could.

Younger siblings learn from what they watch, and what they watch most closely is how the older one handles being wrong. An apology from someone with a bit of authority shows that admitting a mistake does not cost you standing. That is a rare thing to see demonstrated. It tends to get copied for decades.

Think of the last time you were short with him and go say the plain version, without adding what he did first. It will be awkward for about ten seconds. He will remember it much longer than that.