I have the same problem.
continuing on the line of @Greg Haskins, maybe this bash one-liner is more succinct:
cat requirements.txt | while read PACKAGE; do pip install "$PACKAGE"; done
# TODO: extend to make the script print a list of failed installs,
# so we can retry them.
(for the non-shellscripters: it calls pip install for each of the listed packages)
the same note on the dependancies failure applies of course here!