Agreed, a cockroach can't survive on Mars anywhere as far as we know. It needs oxygen. For the most part the sorts of creatures we can expect on Mars are lichens, green algae microbial films.
There are also some tiny millimeter scale multicellular "animals" that can survive without oxygen, and a few worm like creatures that can manage with hardly any oxygen. So maybe there could be animals of some type on Mars as well, but our insects couldn't survive there.
Of course - that doesn 't rule out the possibility of some habitat with more oxygen, say in a cave below the surface or whatever. We are nowhere near the point where we can say we understand Mars completely, what habitats exist there. But - it would have to be isolated from the surface to have significant amounts of oxygen, because otherwise it would just be lost to the atmosphere, the near vacuum which is the "atmosphere" of Mars. Water on Mars also could perhaps have oxygen in it. Maybe enough for some aerobes? But it would be a little surprising to find a habitat that a cockroach could survive in on Mars, even in caves.