The Springboks' 12-11 victory featured four yellow cards, including one upgraded to red for All Blacks captain Sam Cane for a high tackle, leaving Foster's team with 14 men for more than half the game.
South Africa captain Siya Kolisi was yellow-carded five minutes into the second half for what appeared to be a similar shoulder-to-head collision with Ardie Savea.
New Zealand were also confounded when an Aaron Smith try was cancelled by the Television Match Official for a knock-on on the other side of the pitch.
"We've sent a number of – we've already sent a file into World Rugby for them to make a few comments on," Foster told New Zealand media with a wry smile.
"Hopefully they do."
Foster declined to comment on which areas of the game the All Blacks were specifically interested in.
"Oh, I think you can guess," he said.
The final was Foster's last match as All Blacks coach, with Scott Robertson set to take over.
Having returned to New Zealand from France, one of Foster's last duties will be a review of the All Blacks' performance with his coaching staff, which players will likely be spared from.
"It probably won't be officially (with players). It certainly will be by me and my coaching group," he said.