I had this problem a few years ago when I bought Splinter Cell something or other, the securom protection didn't like the DVD drive and it thought that I had a fraudulent copy. When I bought a new DVD drive, it worked fine.
You might want to return the DVD and get a replacement, either from the shop you bought it from or the manufacturer, as it is probably defective. If the replacement doesn't work, the copy protection doesn't agree with something in your computer, ie your DVD driver or the drive itself might not be supported.
It may also be down to something like having Daemon tools installed or similar, that install a virtual hard drive, these have a knack of interfering with copy protection.
I think that F1 2011 uses SecureRom copy protection, which is picky with DVD drives for some reason, it might be worth doing a google search on this subject, or write a stern email to the manufacturers of SecureRom asking for a more practical solution, or to buy you a new DVD drive for putting you through this trauma.