IIRC most aquatic mammals detect low oxygen directly instead, allowing them to dive for over an hour without panicking. CO2 builds up in the blood, but they can feel their oxygen levels directly.
The urge to breathe you get when you're holding your breath long enough is from elevated CO2 in your blood and the subsequent change in PH (as a comment here already stated). That urge is actually your diaphragm contracting involuntarily, but you can learn to endure that feeling which is the key for apnea attempts. But besides that, there are no almost no other indications before you pass out. Black-outs are quite common in freediving competitions because of that fact (freedivers just ignore the breathing reflex and nothing else tells them when to stop).
O2 saturation may fall 20-40% during your breath hold. You generally won't feel anything until it's too late. The problem is that you won't feel the difference between 99% and 65% saturation and you may black-out at 64% (those numbers are not the same for everyone). The signs you can detect before blacking out are blurred vision, tunnel vision, fingers tingling, metallic taste in your mouth... But, you have only a very small window of time between those symptoms starting and blacking out (literally a second or two if you're lucky).
Interestingly, the window of time depends on the discipline - the more physically engaged you are the window is bigger. The static apnea (just floating face down in water) gives you almost no warning at all while at longer dynamic apnea attempts you have a few seconds when you can "detect" something is funky with your body.
It also means that by hyperventilating, you can reducessubsequent feelings of asphyxiation, because hyperventilation (rapid, shallow breaths) purges CO2 from the blood. However, it is somewhat inefficient at building up oxygen (compared to slow, deep breaths) so it's easy to accidentally asphyxiate yourself that way.
You are totally unaware of your brain shutting down as the oxygen level decreases. People lose the ability to do arithmetic or simple puzzles including blocks in holes, but by the time that happens youre too far gone to recognize what that means.
(The above is just going off my memory of my physiology class from years ago. Apologies if I misremembered something.)