Breathing exercises are not the treatment for panic
Used to calm yourself, breathing techniques help briefly. Used to prevent catastrophe, they become another safety behaviour and keep the fear alive. Here is the difference.

If you have panic attacks, someone has taught you to breathe. Slowly, from the diaphragm, in for four and out for six. Perhaps it helped a little. Perhaps you now carry it everywhere, like the water bottle and the seat near the exit, and reach for it the moment your heart changes. And the panic keeps coming.
Breathing exercises get taught as the whole treatment for panic, and they are not it. Used one way, they help briefly. Used another way, they keep the panic alive.
What breathing does and does not do
Slow breathing calms the body. That is real. Over-breathing during panic produces tingling, lightheadedness and chest tightness, and slowing it down reduces those. If you are in the middle of an attack and you slow your breath, you will probably feel somewhat better, somewhat sooner. As a way of calming yourself down, it works, briefly.
But panic disorder is a problem of interpretation rather than a problem of breathing. A harmless sensation is read as a catastrophe, the alarm fires, the sensations intensify, the reading is confirmed. Breathing does nothing to the reading. It reduces the sensations for a while, and the reading is still there, waiting for the next flutter.
When breathing becomes a safety behaviour
If you use breathing as a way of preventing catastrophe, if the belief is "I must breathe properly or I will faint, collapse, lose control", then the breathing has become a safety behaviour, exactly like sitting down or checking your pulse. And safety behaviours are what keep panic going.
Every time you breathe your way through an attack and nothing terrible happens, the breathing gets the credit. The belief that something terrible would have happened without it stays intact. You never find out that the sensations were never dangerous, because you never let them run without the intervention. The breathing protects the catastrophic reading instead of challenging it.
I have met many people who have been doing breathing exercises for years, diligently, and whose panic has not improved, and this is why. They were taught a technique for the sensations and never given a treatment for the belief.
The treatment for the belief
CBT for panic disorder targets the mistake itself. We map your loop: which sensation, which prediction, which safety behaviour. Then we test the prediction rather than argue with it.
The heart of that is interoceptive exposure: deliberately bringing on the sensations you fear, in a controlled way, and letting them be there at full volume without breathing them away or sitting down, so that you find out what they actually do. What they do, every time, is peak and then subside, with no catastrophe, because the catastrophe was never going to happen. Once your alarm has experienced that enough times, it stops firing at the sensation.
Using breathing deliberately
I do teach breathing, and I use it, but deliberately rather than defensively. Choosing to calm yourself after a hard day is a tool; reaching for a technique in terror to stop a disaster is a ritual. Part of the work is learning to tell them apart, and, for a while, deliberately not using the breathing during exposure, so that the sensations get to run and the belief gets tested.
Later, once the alarm has recalibrated, the breathing goes back to being what it should always have been: a pleasant way to settle, used when you want to, and not needed to survive.
The same logic for other safety behaviours
Everything said here about breathing applies to the water bottle, the seat by the door, the pulse check, the sitting down, the leaving early. Each brings relief and leaves the belief intact. We unpick them all, gradually, and the places you have been avoiding come back in steps you control.
If you have been breathing through it for years and it has not changed, there is more on how I treat panic disorder, and on why the sensations themselves are the way in.