If you would like another way in which to make this sentence parallel, the writer can use parallel prepositional phrases:
As a result of careful planning, many lives were saved with panic prevention and with quick action.
While this sentence is a revision of the relationship of ideas as well which you may not want, it does seem that the careful planning is what enabled the panic prevention and the quick action. So, in order to establish cause and effect, the complex sentence was written.
Parallel structure in sentences is when words, phrases, or clauses are written in similar length and grammatical form. For example, a sentence like "I like swimming, jogging, and to dance" should be written as "I like swimming, jogging, and dancing".
For your sentence, it'd be more proper to say "Careful planning prevented panic, and quick action saved many lives." Notice how the noun phrase and verb phrase in each is similar. Another choice could be "Panic was prevented by careful planning, and many lives were saved by quick action"; however, these two combined sentences are passive rather than active. I recommend going with the first one.