Sympathies with this one - the AI does seem to be particularly keen in this race.
Early in career mode I did find this one of the trickiest circuits/races. Even now it's a struggle to shake the AI off when in almost all other races I can leave them in the dust.
I can agree with @bogdantw - the AWD cars seem to be more effective and some NOS is very useful to beat the AI to the first corner as well as boosting your speed down the straight.
Make sure you have your brakes adjusted to maximise your stopping power without locking up - even without NOS I find I can often sneak up the inside and out-brake a few AI cars. Just make sure you slow down sufficiently so you can turn tightly and stop any AI cutting in on the inside. I even cut over the pavement on the apex if necessary just to get ahead of the AI.
One subtlety to this circuit, you may or may not have noticed, is half the circuit is a lower friction surface - it looks and feels like it's perhaps a simulation of a concrete roadway.
The section starts on second corner after the hairpin - as you turn left and then head toward the section that goes around that globe/sphere thing. Your back on regular tarmac just after the 90-degree left-hander at the end of the straight after passing the globe thing.
This corner is where I find it most apparent - I was forever missing the apex and ploughing wide into the barriers on this corner exit - I still have to remind myself to brake early here (and possibly a little gentler to stop locking-up)
So generally its an aspect to keep in mind through that section - there's less grip so you have to be careful how much speed you try to carry into the corners around there.
I still find it tricky nailing that last section with crested-90-degree corner before the long home-straight - there's a lot of steering, braking and gear changing to get right in that bit all at the same time - especially when you have the AI breathing down your neck filling your mirror!
And as always on any circuit it's important to get nicely lined-up to maximise acceleration out of the last corner, and hence maximise the speed you carry down the long straight.
I've since managed to win the C-class race (Hard AI) with various cars: FWD Focus RS, RWD Lotus Exige S, 911 GT3, Ford GT500, Caterham R500.
The AWD's are easier though: Audi TT, S3, R8. Not tried the STi or Evo's yet.
I find the Nissan GT-R's particularly effective - I can get a 3-lap race time in the low 2:40's both in a C999 R34 (with NOS) and a C998 R35 (without NOS) without too much trouble.
Hope this helps