One would think that a Cadet would inform their superior officer of such a discover particularly when a single Romulan vessel manages to destroy 47 Klingon ships. No wonder Narada was able to attack Vulcan so easily...no one was informed of it until it was too late.
To recap, it's a simple thing to read between the lines of the dialogue quoted above and to see that her superior officer was
informed, after which Uhura was sent home for the remainder of her scheduled shift, and that there was nothing in the intercepted transmission which mentioned a Romulan vessel (or, apparently, any vessel at all besides those 47 Klingon craft which were destroyed.)
Didn't Pine ask her with a swollen tongue if the ship was Romulan, to which she replied 'Yes'? So she knew it was a Romulan ship.