Any time you have unprotected sex, you run the risk of becoming pregnant. Yes, there is a chance that the pregnancy test misread, especially if you took one too early or if it was old or otherwise damaged/tampered with. Also, if you pee too much on the stick it could cause a misread. Taking a home pregnancy test about a week after your missed period and taking it first thing in the morning will increase the accuracy of it. If it is still negative but you feel it should read otherwise, see your doctor as he/she can perform a blood pregnancy test, a more accurate and more sensitive to the pregnancy hormone (HcG) test.
If that is negative, chances are your period is late due to stress, changes in diet/sleep habits or just a slight hormonal change, especially if you just started having your periods.
However, if you continue to miss your period, go back to your doctor, who can perform another blood pregnancy test and may order a transvaginal ultrasound to detect any problems inside your uterus or to detect an early pregnancy.
Good luck!