To resolve the issue, Core should be upgraded manually. To do that either download the new Core installation package from https://support.quest.com or https://rapidrecovery.licenseportal.com
Alternatively, just go to C:\Windows\Temp folder, sort files by date and find Core<version>.exe installation package. It's usually about 1.7GB in size (for 6.2.1 version). Just copy the file into any other folder.
Note: if Core service is not running but MongoDB is running, then please stop the MongoDB service (error will be shown). After that just start the Core service again.