The following articles suggest that dinosaurs breathed efficiently, like birds do still: which allowed them to cope with low oxygen levels that killed off other species.
Note that some birds are able to breathe and fly at 20,000 feet, where the oxygen is lower (less than half sea-level pressure).
BBC Earth - Did all dinosaurs breathe like birds?
BIRDS EVOLVED from carnivorous theropod dinosaurs.
Living birds have a very unusual system of respiration, which sets
them apart from all other animals: their lungs are unidirectional.
In birds, the unidirectional nature of the lung means that air with
oxygen passes through the lungs during inhalation and exhalation.
Birds can do this because they have a system of air sacs that connect
to the lungs, which store air during the entire breathing cycle.
During inhalation, oxygen-rich air passes through the lungs directly
from the trachea, but during exhalation other oxygen-rich air that had
been stored in air sacs passes across the lungs.
Their lung is remarkably efficient at getting lots of oxygen into the
blood. This is important because birds fly, and flight is an activity
that requires a lot of energy and an elevated metabolism, both of
which require a large quantity of oxygen.
So did dinosaurs have this type of lung? Some dinosaurs definitely
did. We know that because the air sacs often leave characteristic
traces on the bones, which fossilise.
In many birds and dinosaurs the air sacs are actually inside the bones
themselves, hollowing out the centre. We can see these internal
sinuses, as well as the circular or oval-shaped openings that lead
into them, in many bones of theropod and sauropod dinosaurs. This is
clear evidence that they had a bird-like lung.
We are not so sure about ornithischians, such as the horned dinosaurs
and duck-billed dinosaurs. Their bones do not have the hollow centres
and circular or ovoid ‘foramina’ that are so often seen in the bones
of theropods and sauropods. This may mean that ornithischians breathed
very differently compared to other dinosaurs.
This is an important question about dinosaur biology that is currently
the subject of much research by palaeontologists, so keep your eyes
ABC Science - Did low oxygen give dinosaurs a boost?
Low oxygen levels could have triggered two giant extinctions hundreds
of millions of years ago, allowing the dinosaurs to reign supreme over
the ancestors of mammals, a U.S. researcher says.
University of Washington palaeontologist, Dr Peter Ward, presents his
argument to a meeting of the Geological Society of America in Seattle,
Washington this week.
Dinosaurs first appeared during a long period of low oxygen and
therefore developed highly efficient breathing mechanisms that allowed
them to thrive while many other species became extinct. Ward arrived
at his theory by tying in what is known about the physiology of
dinosaurs with recent geological evidence suggesting that from 275
million to 175 million years ago, oxygen levels stayed very low -
comparable to levels found now at altitudes of 4,200 metres.
Ward believes low oxygen and hot greenhouse conditions caused by
intense volcanic activity may have caused widespread extinctions 250
million years ago, at the boundary between the Permian and Triassic
periods, and about 200 million years ago, at the boundary between the
Triassic and Jurassic periods.
Ward said he put together three pieces of the puzzle - the extremely
efficient breathing systems of birds, the finding that many dinosaurs
had similar physiology, and a report that came out earlier this year
showing that oxygen levels were low during the two extinctions.
"Someone told me they had heard of or seen geese flying above [Mount]
Everest - at 31,000 feet [10,000 metres]," said Ward, pointing out the
air at this altitude was very thin. "If you put a human at 30,000 feet
they'd be very, very, quite dead. And the birds are not only up there,
they are doing major heavy exercise."
Birds and dinosaurs both have holes in their bones. And many of the
largest dinosaurs, such as brontosaurus or apatosaurus, seem to have
had lungs attached to a series of thin-walled air sacs that may have
acted something like bellows to move air through the body.
"The reason the birds developed these systems is that they arose from
dinosaurs halfway through the Jurassic Period. They are how the
dinosaurs survived," Ward said. "The literature always said that the
reason birds had sacs was so they could breathe when they fly. But I
don't know of any brontosaurus that could fly."
"However, when we considered that birds fly at altitudes where oxygen
is significantly lower, we finally put it all together with the fact
that the oxygen level at the surface was only 10% to 11% at the time
the dinosaurs evolved." Currently at sea level, atmospheric oxygen
levels are 21%.
If giant dinosaurs had to breathe in a low-atmosphere environment,
then such an efficient breathing system would have given them a
"You'd be really favoured for survival in very bad, nasty, low-oxygen
world," Ward said.