When you are called on the carpet, you are usually questioned by someone in authority. In most cases, you are rebuked and are held accountable for a mistake or an offence.
Example:
The students were called on the carpet for cheating in the exam.

In the old days, most offices did not have a carpet. Only the most important people in the organization were given one. Therefore, when you say that someone was called on the carpet, what you mean is that a person in a subordinate position was called to the boss' room to face the music. The person literally stood on the carpet while the boss gave him a piece of his mind.