Is there any automated go-around procedure?
For go-around, several things have to be done in the moment the decision is taken:


Apply full power (obviously),
disconnect autopilot glide-slope mode,
disarm spoilers and retract them if they are extended,
disarm autobrakes and
in some aircraft reduce flaps.


Modern airliners, and some smaller aircraft, have a method for doing all of these at once via the TO/GA button. On Airbus aircraft it is done by just advancing the thrust levers to the TO/GA (full power) position, but on Boeing aircraft and many other types it is a separate button on or near the thrust levers.

So if the crew "apparently decided to undertake this procedure manually" it means they moved the thrust levers forward and started changing the other things. And probably missed one of them.

Notes:


I am not sure whether lateral mode remains under automatic control or not and it probably depends on aircraft as some can connect autopilot to only roll or only pitch and others don't. Pitch control is manual immediately after go-around in either case.
The last flap setting usually adds a lot of drag and a little lift. In some types the drag is too large and the flaps have to be retracted to the last usable position. On other aircraft they can be used in any position and have to be left were they were to avoid loosing lift.