What tires are you running? Get some fresh bilsteins struts, along with h&r lowering springs. Fresh race/sport brake pads and rotors, stainless steel brake lines, flush brake fluid. If you have the money get some 18x8.5 wheels along with 245 40 18 or 245 35 18 tires
I cant stress enough when it comes to the basics of handling... and going fast around a corner a huge huge part of it is tires, brakes, and of course not having blown to **** struts.
Don't beat yourself up too bad, you don't know how often he drives that road. I never lost a race or competitive driving on this 16 mile backroad I drove almost everyday. I drove a 140hp 318i which is no high performance car. Until one day I couldn't shake a 1987 porsche 911 turbo off my ass... he lived in his house on the road for the past 20 years.
6 months later I ran into him again but this time I was in my e39 m5 so I got revenge passed him on the straight and then he couldn't keep up
Moral of the story
Get to know your car, the road, tires,brakes,struts then power