On Tuesday night, the Scottish giants lost 2-0 to a team who finished in fourth place in Luxembourg's top flight, and it meant that they bowed out of the competition in the first qualifying round.
Rangers have been ridiculed on social media after arguably the worst result in their history, and Rossiter has admitted that the humiliation will never be forgotten by their supporters.
The 20-year-old is quoted by the Daily Record as saying: "There are no words for it and no excuses. I can't apologise to the fans enough. I don't think they will forget this and we won't forget this.
"A trophy is the main thing and we need to try to win as many games as possible and as many trophies as possible. I don't think anything can put it right but we need to do our best to try."