But Ms Morris, herself a former teacher, insisted there had still never been a better time to join the profession.
She re-entered the Government last month following a period on the backbenches after her decision to quit as education secretary in October 2002.
Her belief that children in the 21st century face an era of change that their parents and grandparents find difficult, if not impossible, to understand has been a common theme in her speeches both before and after her resignation.
The drugs threat, as well as a determination to cut truancy and street crime, spurred Ms Morris to experiment with stationing police in schools in deprived areas. The scheme could be expanded in the next few years.
"The challenge they face is not the cigarette behind the bike shed, it is crack cocaine on the street corner or in discos. It is the equivalent temptation for teenagers to those that were coming my way in the 1960s," she said, in a speech marking the end of centenary celebrations of the Institute of Education, University of London.
Teachers need the skills to be able to prepare their pupils for such a world, and this meant that they would have to undergo regular training throughout their careers.
She said: "For every profession, there is a time in the cycle of life when the time is theirs, when the world is focused on them, and they are more important than ever, ever before.
"For us in education it is now a time when the world has realised that the future really is about learning and teaching."
That was why it was a "huge joy" as well as a "huge challenge" to teach in this period, she said.