Is it in your job description to do this kind of thing? Basically... are you the skivvy? If the answer is yes.. then you didn't do your job, so yes, apologise.
However, I think what may have happened, is that by showing your manager up by telling him to basically 'get it yourself', he was embarrassed that he'd asked you to get whatever it was he wanted, and reacted the way he did because of that. In which case.... sit on it. Dont apologise. He spoke to you in a very bad mannered fashion in front of your colleagues, and should be left alone to cool off and have a good think about the way he behaved.
If and when he does apologise, just explain your actions, that there was no hidden malicious intent behind your comments, and that you are ALSO busy, and to suggest that he is busier isn't very helpful or condusive to good working relationships.
Tomorrow it'll seem like nothing,, and I'm sure you'll be joking around again in no time.