Faletau was allowed to feature in a 24-22 victory over the Springboks at the Principality Stadium on December 2 despite the Test falling outside World Rugby's international window.
Bath had been aware that sanctions could be imposed for giving the number eight the green light to line up for his country.
The Premiership club on Wednesday confirmed they have been slapped with a fine and called for a change of regulations.
Bath chief executive Tarquin McDonald said: "We understand Premiership Rugby's position on this, and have subsequently worked proactively with them to swiftly achieve a fair resolution.
"We believed this situation would change, that has not yet happened and we have therefore come to an appropriate settlement with Premiership Rugby.
"However, we continue to believe that there is appetite for change and that this ongoing conflict between the club and international calendars is not good for players, clubs or unions.
"We continue to support the objective of a solution for the separation of club and international calendars in a way which benefits players, clubs and unions, and brings an end to situations such as this."
Photo Getty Images. Caption: Wales number eight Taulupe Faletau