Hi there, as you mentioned that your Mac was released in 2011, I guess that the macOS can't repair the disk occurs because it endures such a long time use. There is less possibility to repair the hard drive for further use. Since the old Mac was no longer in use and not the current backup, you can totally ignore that error message or you can replace the hard drive if you want to utilize it still.
All drives are meant to fail, some have failed already while others are going to fail. In order to avoid data loss caused by drive failure, a regular backup is necessary. You can make use of the Time Machine to complete that work. If you fail to back up important data on your device, iBoysoft Data Recovery Software is recommended for you to scan for lost data from inaccessible, corrupted, unreadable, and even failing hard drives.