Historical records from the year 1054 are available (and are of course the reason we date the nebula to "1054" rather than "the eleventh century"). You can just go see what people of the time thought.
Wikipedia doesn't quote the records associated with 1054, but does quote the record of a supernova in the year 185:
> In the 2nd year of the epoch Zhongping [中平], the 10th month, on the day Guihai [癸亥] [December 7, Year 185], a 'guest star' appeared in the middle of the Southern Gate [南門] [an asterism consisting of ε Centauri and α Centauri], The size was half a bamboo mat. It displayed various colors, both pleasing and otherwise. It gradually lessened. In the 6th month of the succeeding year it disappeared.
( https://en.wikipedia.org/wiki/SN_185 )
What people thought appears to have been "sometimes there are new stars, but they go away again".