An engine control module includes a deceleration fuel cutoff (DFCO) module, an actuator control module, and a rolling neutral (RN) module. The DFCO module determines whether to disable provision of fuel to an engine when a vehicle speed is greater than zero and selectively generates a DFCO signal based on the determination. The actuator control module disables the provision of fuel to the engine when the DFCO signal is generated. The RN module selectively generates an RN mode signal in response to a determination that the DFCO module is not generating the DFCO signal. The actuator control module controls the provision of fuel to the engine based on a desired engine speed when the RN mode signal is generated. A transmission control module disengages first and second input clutches of a dual clutch transmission (DCT) to decouple the DCT from the engine when the RN mode signal is generated.