Right Way Up:
If you go-around at minima, you pitch at a normal rate towards approx 15 degrees which will take roughly 4-5 secs. At the same time the engines will be spooling up towards TOGA and again that will take roughly 5 seconds. The engine thrust increase should be quick enough to maintain speed whilst carrying out the pitch manoeuvre. The altitude loss if the manoeuvre is carried out correctly will be roughly 20-30 feet. Even allowing for 3 secs pilot delay the total loss will only be 50-60 feet which is still safe if not advisable. If a pilot delays more than that then you cannot account for that behaviour or lack of ability. It is quite safe and proper to go-around at minima.
Sounds like you're speaking of a missed approach from DA on a vertically-guided IAP. There should be no altitude loss on go-around from MDA on a non-precision IAP. Further, in either a DA or MDA missed approach the engines should already be sufficiently spooled up to provide a significant increase in power in far less than 4 to 5 seconds.
Also, in the case of an approach with a DA, the missed approach obstacle clearance criteria provides for a height loss below DA for a prescribed distance before the missed approach obstacle clearance starts its slope upwards.
In the accident at issue it would have been an MDA which should have resulted in no height loss unless the decision to miss was made subsequent to descent below MDA (always a dicey situation in poor visibility.)