Sporting had battled back from 3-1 down to level the scores at 3-3 when Klaas-Jan Huntelaar's header was adjudged to have hit Jonathan Silva's arm and Eric Maxim Choupo-Moting scored the resulting penalty.
Television replays showed, however, that referee Sergei Karasev had got the decision wrong and the ball had in fact hit Silva on the head.
Sporting have now confirmed they will appeal to UEFA, with Schalke issuing a statement saying that the Portuguese club want either a replay or the game to be deemed a draw.
"The 4-3 home win in the Champions League is being disputed by Sporting CP," read a statement on the Royal Blues' website.
"Last season's runners-up in the Portuguese top flight aren't happy with the result on Tuesday night (October 21st) and have therefore lodged a protest to UEFA.
"Sporting CP have requested to the European football association that the game be replayed and have alternatively requested payment of the premium for a draw.
"The visitors are protesting a penalty given in injury-time, which they believe was unfairly awarded. Eric Maxim Choupo-Moting then converted from the spot to give the Royal Blues a 4-3 win.
"FC Schalke 04 have been asked by UEFA to give a statement and it will be made shortly under consideration of the protection of the club's interests."
In their own statement, Sporting proposed that video technology should now be used for the fourth official to review decisions and called for a "serious review" to be carried out.
"Despite our best efforts, we were not permitted to secure the desired result," the statement read.
"As is publicly known, Sporting have been working hard in the presentation of concrete proposals for the improvement of football, including the introduction of new technology such as the possibility of the fourth official reviewing images during the game that allow the main referee to avoid errors which discredit the game.
"The reality is that such incidents make us all the more certain that we are on the right track. More than just thinking about people, it would be fantastic if a serious review could be made of substantial and structural proposals for the improvement of football and sport in general.
"In light of the incidents against our team in the Champions League in the match with Schalke 04, Sporting SAD have decided to present a complaint to UEFA."