The phrase "admitted that the system" is correct and usable in written English.
You can use it when discussing a confession or acknowledgment regarding a system, often in a context of evaluation or critique.
Example: "The engineer admitted that the system had several flaws that needed to be addressed."
Alternatives: "acknowledged that the system" or "conceded that the system".
"You've all admitted that the system failed; none of you feel personally responsible.
But he also admitted that the system was difficult to adjust to.
The government has admitted that the system is flawed and, two weeks ago, introduced tougher measures designed to root out false applications.
The government said as much itself in its misnamed 1998 White Paper on asylum ("Fairer, Faster, Firmer"), which admitted that the system was being abused by people migrating for purely economic reasons.
One day after college football's system for creating a Division I-A national title game collapsed beneath the weight of its own complexities, nearly every constituency involved with the Bowl Championship Series admitted that the system was flawed, and some vowed change.
"You've all admitted that the system failed; none of you feel personally responsible," Mr. Waxman said, addressing Mr. Rumsfeld, who resigned as defense secretary last fall, as well as one currently serving general and two retired ones who also testified under oath Wednesday.
Even college administrators who must watch the bottom line admit that the system has drawbacks.
But despite a flurry of arrests, investigators admit that the system of monitoring is undermined by corruption and legal loopholes.
But even supporters admit that the system, also known as cap and trade, is falling far short of that goal.
Angie Motshekga, the schools minister, admits that the system is largely "in crisis" and will take 20 years to fix.
Words such as "profits" and "capitalism" are coyly placed in quotemarks, as though the book is reluctant to admit that the system it so ardently advocates actually exists.
