Savtaro:
You asked what happens when the price falls after you purchased the ticket and I told you that carriers are under no federal obligation to do so.
When you purchased your ticket, you locked in your price at the current rate. Now if a carrier wants to provide the price difference, they are free to do so and in whatever manner it chooses.
As for Continental's Low Price Guarantee... information can be found
here. However, I do not think that you meet the terms and conditions since you would have needed to contact the carrier by midnight the day you purchased the ticket.