To some extent it's not really possible to write a story without three acts. Unless it's only two sentences long it will always be possible for a reader to post-rationalise a beginning-middle-end structure onto your tale. But when writing, don't worry about it.
You don't need any acts in a short story. You are free to pick even the smallest atom of structure and explore your idea there.
The expectation is that a short story will be short, and readers will be happy, even grateful, for a story which gets to the heart of its idea quickly, and wraps up when the point has been made.
Suppose you were to have a really interesting idea for how to escape from handcuffs, you could construct a short story which starts with a villain embarking on a prematurely triumphant monologue, and end with that same villain's reaction when the hero appears at his neck with a hot poker.
Such a story spans just a small fraction of a traditional third act, but it would still be satisfying, and readers could still, if they wanted to, perceive it as a three act story.
Following clarification of the question, here's some thoughts on adding a whole extra act to a completed story. I'm going to talk about movie scripts here, because I find structure to be far more visible in those.
If you feel your story lacks a middle act, it's probably because it lacks the story elements traditionally found in the middle act. If you're struggling to figure out what those elements are, you can try analysing other stories.
Try thinking of a familiar movie in the following way: strip out the middle act and try to make the plot make sense without that act. Here's an example using a story everyone's familiar with:
A young space farmer longs to leave his dull planet and join the Rebellion against the evil Empire. He meets two robots who happen to be on a mission on behalf of the rebellion. The robots lead the boy to a mentor who takes them all to a rebel base where the hero joins an attack on the Imperial space station.
Now try to imagine that movie got made, and the producers watched it and realised that, although it made perfect sense, it was dull, and empty: the hero just discovers a problem and goes directly to the source and solves it. It just doesn't feel like a full story. And suppose, to fix this, they went away and filmed a second act to fill the gap. What processes would they have had to go through to concoct that second act?
Instead of the boy going straight to the rebel base, his mentor takes him to a bar where they get in a fight, meet a ruthless space smuggler and get in another fight. They go where the mentor suggests but they find that place had been destroyed and many people killed. Then they get captured by some bad guys, and they meet an idealist princess and sneak around trying to avoid more fights. Doing all of this raises the stakes (the mentor dies), introduces different approaches to consider (selfish / idealistic) but it also teaches the hero the skills and confidence for his later battle.
For yourself, pick a familiar story in your genre. Strip out the second act, smooth over the join and see what the story would look like. Note how relatively easy it can be to make that shortened story make sense, but note also how it loses its heart, soul or purpose. If your story has the same shortcomings, then yes, you are missing an act. Now you already have the answer for what that writer would have had to do to add a second act. Take inspiration from that.
You'll probably find, in many stories that you analyse, the second act is about punishing the hero's (and reader's) naivety or misconceptions, and teaching him/her a more effective response to the story's main problem, but also giving him/her alternative choices to consider. You may find it quite easy, since without a second act your hero may be walking into 'battle' fully equipped and prepared, which is boring. For your new second act you would take that preparedness, analyse it, strip to down to nothing, show the wrong-headedness of it, and build it up again into the potential for something better or something worse. (It's only a potential, because the third act is where we finally discover if the hero can realise that potential.)
That's only a taster. You can read up on it all over the place, but the above is a technique I've used in your situation to help me clearly grasp what the second act is about.