Just keep on trucking, looking for another job. It's their loss!

Apply at their competitors business!

Maybe they thought you were being sarcastic.

I'm sure you'll find this insight VERY useful.

I'm sure he won't, though.. :/

Or it was just an excuse because they couldn't say why or didn't know why they had rejected OP. It's basically impossible to prove wheter OP showed interest or not, which makes it a good excuse.

Words aren't enough all the time.

It's not really so much what you say but how you say it. Body language can show confidence, enthusiasm or indifference.

Next time don't be so sarcastic.

Either you really didn't seem that enthusiastic - maybe it was nerves, maybe you only said cliche phrases, maybe your definition of enthusiastic is different than theirs. Or, more likely, they interviewed a very high number of people and either just forgot who you were specifically (not that that's any better) or you just weren't the best candidate, but there was no specific reason. E.g. you were as good as someone else, but they had to choose someone on gut instinct and just had to give you a generic response. Don't think too much of it and keep applying

HR people are generally fucking idiots who have their own agenda!

When I say that as the reason I deny candidates it has more to do with the tone, body language, and energy level of a candidate.

I wouldn't hire someone who doesn't understand sarcasm either.