The striker played the final 24 minutes of Tuesday afternoon's 0-0 draw between the two sides in their Group G opener in Port Elizabeth just 10 days after fracturing his ulna in a warm-up game.
Ivory Coast officials sought and were granted permission from FIFA for Drogba to play wearing the dressing, but while Portuguese coach Queiroz insisted there was no controversy over the issue, he admitted his surprise at the decision.
He said: "It's not for us to decide whether Drogba should play or not, it depends on FIFA.
"During the delegates' meeting which was held, the FIFA delegates decided the referee's decision was final. That was a bit odd as far as we were concerned.
"There are rules and regulations and for example, sometimes players can't play wearing a string bracelet, but a player can fracture his arm and play with a plaster cast and put at risk the Portugal players.
"I would like to know if the rules are the same for everybody.
"If you can't play with a simple string bracelet and somebody can play with a strapping as Drogba did, that's a little bit unsusual.
"Maybe the rules will be changed now, we don't know."
Drogba later revealed it was his decision to be included among the substitutes, and said he could be ready to start against Brazil in five days' time.
The Chelsea striker said: "It was everybody's decision, but yes, my decision to play and say to the manager that if he needed me, I was going to be there.
"I could be ready. We have five days to prepare for this game, so I am there."