Speaking yesterday at the association's annual conference at the University of Warwick, Angus Laing said that the disciplines had achieved "totemic status" in government, but were not sufficient on their own to create growth.
High-cost STEM courses have had their teaching funding protected by the government despite the complete removal of direct teaching grant for many other subjects.
"While these STEM disciplines are necessary conditions for innovation, for a flourishing knowledge based economy, they are far from sufficient," he told delegates.
"Britain has a fine and proud research tradition in STEM. We unquestionably punch above our weight. Yet in commercialising innovations, in business development, in building global-scale industry leaders and brands, we lag behind our international rivals," Professor Laing added.
Business schools needed to be seen not as "institutional cash generators" but as "innovation generators for society", he said.
Professor Laing, who is dean of business and economics at Loughborough University, said the "policy discourse" should focus not on STEM but on "STEM squared, where the M stands for management as well as for maths".
The ABS would lobby strongly for the "STEM squared" agenda over the next two years, he said. "It is a message we intend to keep pushing."
He stressed that the ABS was significantly stepping up its policy lobbying efforts and wanted to place business schools at the "core of government strategy for growth". The ABS has set up an innovation taskforce to look at how its schools can boost the economy.
Speaking about the association's influence over policymakers in recent years, Professor Laing said: "We have to plead the case of missing in action. Over recent years the association had lost much of its sense of direction."
But noting the appointment of former 1994 Group executive director Paul Marshall as chief executive in January, Professor Laing said that "over the past year the association has entered a period of radical renewal".