Look at the spec sheet that came with the new radio. If it states that the "pre-amp" outputs are anything less than 4 volts, then the radio speaker wires need to be wired to the amp, else you can wire to the pre-amp output jacks.
( the small round hole is the tweeter )

EDIT: I looked your new radio up on Crutchfield, it does have 4 volt preamp outputs.