Often the patch cable needs to be an attenuating type, when you send a signal to a mic input. The cassette unit expects a very soft (low amplitude), which it amplifies via automatic gain control. As a result your signal is liable to be clipped and distorted.
Of course there is a remote chance that your computer output can be reduced to a soft enough level, and the automatic gain circuitry responds with sufficient attenuation, to record your signal properly.
Even so, a cable tends to introduce mains hum, which becomes audible during soft passages in the music. Therefore you still might want to use a shielded potentiometer to attenuate what goes into the mic input.