Angry supporters surrounded the team bus following Rangers’ 2-0 defeat by Progres Niederkorn in Luxembourg with some signing: “You’re not fit to wear the shirt.”
Rossiter was making his first start in more than 10 months after recurring calf problems kept him out for the vast majority of last season while six of Pedro Caixinha’s eight summer signings featured in the Europa League defeat, but the former Liverpool player insists all members of the squad share the fans’ pain.
The 20-year-old told Rangers TV: “We are all not going to forget this for a long time and I know the fans certainly won’t either but the lads are already speaking and saying we need to get together now, show a bit of courage and come out of this.
“We need to prove to these fans that we want to be here and we are good enough to wear that Rangers shirt.
“We would have liked to have beaten them by more in the home leg but with a 1-0 victory we were confident of coming here, putting on a show for the fans and winning the game - and that just hasn’t happened.
“The lads are really feeling it in there, the new lads and the lads who have been here for a while.
“Listen, whether this is my first game for Rangers or my 50th game for Rangers this is massively disappointing and I can’t apologise enough.”
Progres had never won a European tie before and had only scored once, against Glentoran, in 13 matches in UEFA competitions before the second leg. Rangers hit the bar three times at the Stade Josy Barthel but struggled to impose themselves on their opponents for large periods of the two legs.
Rossiter added: “It is massively disappointing, I cannot apologise to the fans enough, we simply weren’t good enough and all the lads know that.
“I can stand here and say we were unlucky with this or that but listen, we weren’t unlucky we simply weren’t good enough on the night.
“We know we have let ourselves down and we have let the whole club down and we have let the fans down who have paid good money to come out here and travel.”
Rangers are now set to sign Graham Dorrans from Norwich but the first qualifying round exit is a major financial blow after loans from directors and shareholders helped finance their major summer squad rebuilding project.
They also have no friendly games organised before they open their Ladbrokes Premiership campaign against Motherwell on August 5 and Caixinha will need to re-examine his pre-season programme.