First of all: In principle, plastic yoghurt pots belong in the yellow bag or the recycling bin. This is the only way to collect the packaging and process and reuse the material afterwards.
You should always disassemble the mug into its individual parts. This means: Remove the foil lid as well as the paper streamer, which is usually stuck around the cup. The paper then goes into the wastebasket, the plastic cup and its lid go separately into the yellow bin.
This method of elimination has an important reason. This is the only way for waste management companies all over Germany to recycle properly. Leaving the lid on the yogurt pot complicates the recycling process.