Yep. Apparently you removed the original joining pin when you took the chain off for cleaning. These are NEVER to be removed. If you do remove the chain, break it by removing one of the "standard" pins and replacing it with another specific joining pin or a master link. At this point, your chain is a failure waiting to happen unless you can find and remove the pin you just pushed out and replace it with a master link.

BTW, master links are definitely the way to go if you want to remove the chain for cleaning. KMC and Wippermann Connex links are compatible with Shimano chains and SRAM, KMC and Wippermann chains come with master links.