I've heard it a lot, and of course asked myself the question upon seeing no birds or reptiles. But during a debate of the movie afterward I came to the conclusion.

Birds, Lizards, Aquatic mammals and whatnot would not have fit with the clear-cut predator/prey distinction of the movie.

They are creatures which vary wildly between being Carnivore, Herbivore, and Omnivore, and would have muddled the overall tone of the movie had they been included.
If you see a tiger, wolf bear or even an otter and know anything about them, you can automatically link them with being predatory. They eat other living creatures to survive.
Likewise look at a goat, elephant, rabbit, or rodent. stereotypically these creatures eat foliage, vegetables and fruits. They do not survive off living flesh.

Now take a bird. There are those clearly on one side. A canary eats seeds and fruit, a vulture would eat flesh or carrion. But what of a crow? They're omnivores that eat anything available to them.

Bearded dragons eat both insect and green foliage.

Most aquatic living creatures are primarily predatory, yes. But their exclusion may be chalked up simply to being non-bipedal.

Basically. The movie's plot demanded that it's cast have a clear cut dichotomy between Predator and Prey in order to work. To have even a background character break that wall would have led to "But what about that guy?" questions, and lessened the overall impact of the story's lesson.

As popular as the movie has been, I've little doubt there will be a series made of it or additional movies. Ones in which we may yet see our favorite animal types. But for the specific story of this version, they would not have fit.