Hey there. Sounds like it could be a couple of things. Are you using manual or automatic gearing? Manual will give you potentially a faster launch from standstill, though of course that depends on the car you choose also (some are slower on launch than others.)
My guess though is the controller. Are you using R2 for acceleration? I think that's a default control - anyway, I found with an older controller that I was falling behind other drivers and that even slower cars were catching up with me on straights. It turned out that the R2 trigger was worn out and as a result was only delivering about 80% power to the car. To test this, you could always re-map the acceleration control to one of the buttons for a test run on a track with a good straight (Scotland's BHR circuit maybe) and see if things improve. If it is that, unfortunately you'll need a new controller (unless it's under a year old) as the trigger buttons are the best for fine control of acceleration and braking.
Let us know how you get on.