When you are introducing yourself to someone new it is not necessary to include the phrase "I've been laid off" or something similar within the first few seconds of your elevator pitch.
Perhaps it is instinct that is directing you to "confess" this information. Perhaps you feel the need to be honest, or maybe it makes you feel better. No matter the reason, please don't do it, for your own good.
Including your employment status in your pitch is irrelevant to what you want in the future. Sharing this information too early neither makes you look more interesting nor talented. It may conjure up other thoughts in the listener's mind that would be distracting from your core message. Thoughts such as:
"poor thing, this is a terrible time to be unemployed"
"wonder what they did that got them laid off"
"how are they ever going to find a job right now"
"wow, it stinks to be you"
Those distracting thoughts can get in the way of the listener being able to help you. Sure, empathy is a wonderful thing, but that's not the help you want from most people. (That's why you have friends, family and a support network).
The other thing to know is that many employed people are looking for new jobs right now too. They don't start a conversation with someone they don't know by saying "I hate my job and I'm looking for a new one", or at least they shouldn't.
You don't have to be unemployed to be looking for a job or to change careers. There are many factors that lead to someone looking for new work. Especially today, more and more talented people have learned that they should always be prospecting their next job/career move. Certainly they don't confess that up front.
Focus instead on why you are great at what you do and what makes you different and memorable. Summarize the value you have you added to organizations you have worked with. Remember, this is a marketing campaign, you want to create a distinct brand and message that will catch attention for the right reasons, you are talented at what you do!