According to Simple Flying from Merdeka.com, the responsibility to contact the airline/airport and retrieve the baggage lies in the hands of the passengers. Considering the large number of lost items that airlines/airports have to process every year, they do not have the resources to proactively find their owners.

You can go back to the gate and talk to the gate officer to ask for permission to retrieve or search for the intended item. Although it is unlikely that you will be allowed back on the plane due to security reasons, the gate officer may be willing to walk to your seat and check if the item you described is still there.

Some airports, especially busy international airports, will have special lost and found desks. If it has been several hours since you left an item on the plane, chances are the staff has already found the item and recorded it with the airport authorities.

"At most airports, airlines have their own baggage service desks near the baggage claim area. This usually facilitates lost baggage, but you can also inquire about lost items at this counter."