The Giants drew just 5830 fans to their match against Adelaide at Skoda Stadium on Sunday.
It was the lowest AFL crowd since 5083 people saw Fitzroy defeat Fremantle in round eight of the 1996 season.
"We have said for some time now that the success of the GWS Giants will be a long road over a long period of time and we are very committed to that work, as is the club," the League's deputy chief executive, Gillon McLachlan, told AFL.com.au.
"The recent turnarounds of the likes of Richmond and Port Adelaide, as two very recent examples of clubs who have had on-field struggles but are now playing much better and drawing much better attendances, always shows us that clubs can turn their fortunes around once the playing side begins to improve."
Both games played on Mother's Day drew poor crowds, with the attendances at the Giants-Crows and Melbourne-Gold Coast matches totalling just 19,134.
"The AFL would have liked to have seen greater numbers at both of yesterday's matches," McLachlan acknowledged.
"But that is reflective of the on-field performance so far this year of both clubs, in combination with the fact that Mother's Day can be a difficult day for attendances.
"The AFL looks at our attendances very closely every week, and we look at the overall competition and how we are progressing, as well as how individual clubs are progressing with their home game attendances.
"Going into round seven, we have had the largest amount of fans attending an AFL season to this point of our history, which is reflective of a really good competition to this point and means we are generally very happy overall with the progress of the 2013 season.
"We have also had a number of games where attendance has not quite been at the levels hoped, and history shows us that usually aligns with teams not performing strongly on the field."
