Additionally, the survey, called "State of the American Manager", found that half of employees surveyed said they had left a job due to a disengaged manager.

The flip side of that coin, Gallup said, is that great managers inspire greatness in their direct reports.

"Managers' engagement has a direct impact on employees' engagement," Gallup said. "Employees who are supervised by highly engaged managers are 59 percent more likely to be engaged than those supervised by actively disengaged managers."

The survey also concluded that women are more engaged as managers than are men, by a 41 percent-to-35 percent margin, and that  "individuals who work for a female manager are also six percentage points more engaged, on average, than those who work for a male manager."

When working for an engaged manager, two-thirds of direct reports said key factors in their own engagement included a manager who worked with them to set workplace priorities and goals, and one who allowed them to soar with their strengths rather than obsessing with their weaknesses and negative characteristics.

"Companies … base hiring and promotion decisions on individuals' past experience or tenure, or they give them the manager job as a 'reward' for their performance in a completely separate role," Gallup said, referring to its theory that employers actively create and nurture poor management talent. "These organizations overlook talent, and when they do, they lose. They spend needless time and energy trying to fit square pegs into round holes. Their managers are not engaged — or worse, are actively disengaged."

For the minority of companies that know how to grow and keep top management talent, the rewards will continue to roll in.

"Naturally talented managers know how to develop and engage their employees. They create enthusiastic and energized teams that focus on moving their company forward and doing right by their customers," Gallup said.