The round doughnut shapped part you picked up is called the release bearing.
You need to replace that, with a new one before you put things back together.
It sits between the fork (the bit you flipped up and down) and the clutch. It pushs against the clutch to release it.
The clutch works like a spring to return it to its resting position, and the tension between the two holds everything in place.
The release bearing will have little pins, or cut outs that fit over pins or cut outs on the fork. But they will only locate the release bearing against the fork, not lock them together.