It's possible that your posture was incorrect, which can cause circulation problems. Or you may not have been putting the correct tension into your posture. If you lay down, or sit too comfortably, your body starts to go into relax/sleep mode, and I'm sure you know how awful it feels to be woken up when you're just getting comfortable. Sitting meditation shouldn't be uncomfortable, but proper tension in in your trunk helps with staying awake and maintaining focus.
When I began meditation, the switch to deep breathing left me lightheaded and tired for a while until my 'normal' breathing adjusted overall.
How were you positioned? What are your normal habits of relaxation, and are you a shallow breather (when you only fill the top half of your lungs, beneath the breast)?