Okay first of all, if you took the pills correctly and used protection for the first week (unless you started the first day of your period) then you should not be pregnant.
Having pieces of stuff in your menses (the blood and stuff that comes out) is pretty normal. Even if you were pregnant, it would be way too small to see anything at all. I don't think you were pregnant.
The pill changes how your body works, by preventing you from ovulating. SO the "period" you get during the off week is actually just withdraw bleeding and not a real period. Still, there is blood and chunks of the covering that formed inside of your uterus during your cycle.
During a normal cycle (and to an extent on the pills) your uterus slowly builds up a coating of blood-rich tissue so that if a fertilized egg comes along, it has a nice place to settle down in and receive nutrients until it builds a placenta. That covering is what comes out every time you have a period. At the end of the cycle, the body goes "oh well, no egg came along; this covering is too old now and useless. Time to get rid of it and start again", and that's your period. Many women get cramps during this initial time of their period, because the uterus is contracting similar as during birth to loosen and squeeze out the lining.
On the pill, this covering often isn't as thick or as well formed, and that's why women often get lighter and shorter periods on the pill. Still, chunks and blobs are very common, and I wouldn't worry.
The color of your period can vary too, from pink, to red, to almost black! It's all blood and tissue.
