ك also uses the rear of the tongue, but slightly further forward than ق. This distinction accounts for their separate makharij.
Compare the kaf in كِتَاب with the qaf in قَرِيب. Do not force kaf into an artificially deep qaf, or weaken qaf until it sounds like kaf.
The exact rear-tongue contact is not fully visible in a mirror. Focus on the sensation of tongue movement and the sound heard from a skilled reciter rather than the shape of the lips alone.