which suprised me as all of our systems seemed to be working normally.
C172, as far as I know, doesn't have sensors to detect damage to things like wing, rudder and stabilizer leading edges. A dent at those places can seriously influence the aerodynamic properties of the aircraft. And there are all sorts of other things that bird strikes can do, but that not immediately apparent and cannot be seen on your engine instruments.
So yes, you will always return and have the whole aircraft checked over, unless there's an overwhelming reason not to (like being shot at, as mentioned above).
Also, any sort of damage to aerodynamic structures will lead to an increase of stall speed or at least a decrease of their effectiveness at low speeds. So you land with a bit more speed than usual, bleeding it off a few inches above the runway. So in case of a bird strike, a very short strip might not be the best choice.