The question that you brought up wouldn't address your question because "if" is not one of the coordinating conjunctions, but it is a subordinating conjunction. The words that introduce each are:
Coordinating Conjunctions: and, but, or, yet, for, nor, so (a helpful acronym is FANBOYS)
Subordinating Conjunctions: after, although, as, as if, as long as, as though, because, before,
even if,
even though,
if,
if only,
in order that,
now that,
once,
rather than,
since,
so that,
than,
that,
though,
till,
unless,
until,
when,
whenever,
where,
whereas,
wherever,
while
The definition of a subordinating conjunction is:
Subordinating Conjunction (sometimes called a dependent word or subordinator) comes at the beginning of a Subordinate (or Dependent) Clause and establishes the relationship between the dependent clause and the rest of the sentence. It also turns the clause into something that depends on the rest of the sentence for its meaning.
He took to the stage as though he had been preparing for this moment all his life.
Because he loved acting, he refused to give up his dream of being in the movies.
Unless we act now, all is lost.
This article from Purdue on coordinating and subordinating conjunctions explains the usage of the subordinating conjunction as follows:
Notice that when the subordinate clause comes at the beginning, it’s necessary to insert a comma.
From this, the correct punctuation of "You can call me if you need me" is:
You can call me if you need me.
If you were to move the subordinating conjunction to the beginning, however, you would need the comma as follows:
If you need me, you can call me.
As Robusto points out in comments beneath the question, there is no universally acknowledged rule governing whether to include or omit a comma after a conjunction at the beginning of a sentence. Robusto reports preferring to include such commas in academic documents, but many other writers and editors would not include them.
In my experience copyediting manuscripts for book publishers (including university presses) and later for magazine publishers, I don't recall ever having encountered a house style that required adding a comma after "And," "But," or the like. To the contrary, most house styles either said nothing at all on the subject or recommended omitting such commas, presumably for the reason that Words Into Type, third edition (1984) gives at the start of its long section on comma usage:
A comma should be used only if it makes the meaning clearer or enables the reader to grasp the relation of parts more quickly. Intruded commas are worse than omitted ones, but keep in mind at all times that the primary purpose of the comma is to prevent misreading.
The argument for including a comma after an opening conjunction is not, I think, grounded in a desire to make the meaning clearer (since the meaning tends to be quite clear without the comma, as Peter Shor indicates in a comment above), but rather in a desire to demarcate with exactitude the boundaries of the parenthetical expression that follows. Why Gregg Reference Manual would insist on such precision at the beginning of a sentence but not in the middle of one is a mystery to me.
There is nothing inherently wrong with using commas to break out parenthetical phrases regardless of where they appear in a sentence: It increases the number of commas in a work while (arguably) not making the sense of the text any clearer; but it's a style decision, and style decisions—if followed consistently—don't need to be justified.
On the other hand, if you don't want to add a comma after a conjunction at the start of a sentence, I don't think that you should consider yourself to be under any obligation to the preferences of Gregg Reference Manual unless your publisher has instructed you to obey it.
Best Answer
“I'm not superstitious, and thought nothing of it” is no more a complex sentence than is “I went down to the café and ate“. There is no dependent clause here, nor is there a subordinating conjunction. There is a coordinating conjunction and a compound predicate. Those sentences are neither complex nor compound.
That said, it is unusual but not unheard of to use a comma before the conjunction in a compound predicate. This normally indicate a slight pause in speaking; a stronger pause might use a dash. It can also sometimes be used to disambiguate what might otherwise lead to a wrong parse in certain garden-path sentences.