Earlier this month, Samoa's Prime Minister and rugby union chairman said their union was bankrupt and could not afford to insure their players or pay the head coach's salary but World Rugby has since dismissed those claims.
England prop Mako Vunipola had proposed that the hosts' players make a small donation to their Samoan counterparts but the proposal was rejected on Wednesday following discussions among England's senior squad members.
"It's above our station as players," Cole told the BBC. "We play the game against the opposition, whoever we play, and it's not for us to get involved in the politics of paying people.
"You need to go above players, you need to go to the unions, you need to go to World Rugby, and you need to address it at that level rather than just making this an England versus Samoa issue."
The 30-year-old also said that sharing match fees would raise ethical questions in the future.
"(The decision) was along the ethics of paying an opposition to play against you and the future issues it might create," Cole added. "Not so much opposition asking for pay but it potentially looks like: 'We've paid you before, now you owe us a favour.'"
England's Rugby Football Union (RFU) will generate about 10 million pounds ($13.30 million) from Saturday's game and had said those fees could not be shared with Samoa under World Rugby rules.
The RFU pledged to donate 75,000 pounds to Samoa and cover all of their on-the-ground costs.
Samoa have lost both their autumn internationals so far and have slipped to 16th in the world rankings, while England have beaten Argentina and Australia in their last two games.
(Reporting by Aditi Prakash in Bengaluru; Editing by Ken Ferris)
