Why can't you use your shifter? Note that you need to have the shifter plugged into the correct USB port before you start the PS4. You can't switch from anther game to AC without restarting the PS4. I don't know why this is - it caused me a lot of confusion & frustration until I figured it out.
The other thing about AC is it requires you to throttle up in order to downshift successfully in the manual cars. This adds a whole level of challenge to the driving. In all the GT games you can slam your way through the gears with no consideration to the engine revs. AC requires much more precise shifting & it emulates the difference in shifting between the different cars ... so an older car, like the Ferrari F40 or the RUF Yellowbird require you to shift more slowly, moving the gear shifter into neutral before moving to the next gear. If you mistime it the car won't shift & the gears grind mercilessly. PCars2 does not do this, although it does engine brake unpleasantly if you don't adjust the revs as you **** down.
By the way: "if you don't adjust the revs as you shift down"