As the title suggests, does a statement have to mock someone or convey contempt in order to be considered sarcastic? I thought the main criteria was that the statement should mean the opposite of what you really want to say.
Specifically, I recently changed ISPs and discussed the exhaustive selection process for a new one with some friends. After a minor issue arose immediately after connecting to the new provider I said to the same group of friends
Time to find a new ISP.
I believed this to be sarcasm as I clearly had no intention of changing ISPs again so quickly, but have been told it doesn't qualify as sarcasm because I wasn't mocking anyone.