The Light Blues missed out on a return to Hampden Park for next month as a rampant Hibernian side eased to a 3-1 victory and booked a final appearance against Celtic.
A sublime first half hat-trick from Martin Boyle sent the Easter Road outfit into a dominant 3-0 lead before Scott Arfield handed the Gers a lifeline.
However, captain Goldson, who blazed over from just a couple of yards in the closing minutes that could have set up a tense end to the match, sensationally claimed they were out of the contest by half-time.
The centre-back admitted Rangers poor performance had nothing to do with Steven Gerrard’s sudden departure for Aston Villa.
Speaking to Premier Sports in his post-match interview, he said: “We didn’t deserve to win the game. At Rangers our standards need to be so much higher.
“Defensively we were poor. Three chances, three goals in the first-half. You can’t give yourself a 3-0 mountain to climb.
“Attacking-wise, we didn’t create anything, again. As a team at the minute we’re not performing. It’s as simple as that.
“Back to front, not one individual can come off that pitch and hold their head high. We’ve got a lot of work to do.
“The staff have been brilliant and covered everything last week. We’ve let ourselves down. Players don’t follow instructions.
“The first two goals are both from a corner. People are in the wrong position, something we worked on yesterday. From a throw-in, people were in a wrong position.
“And if players don’t want to follow instructions then we can’t blame coaches as they gave us the information to do a job.
“So we’re 2-0 down and they scored a third goal and the game’s over. We can be in there at half-time and say ‘believe in ourselves, blah blah blah’ but it’s over when you’re 3-1 down at half-time.
“That’s nowhere near good enough.”
With new boss Van Bronckhorst watching on from the stand, the Dutchman will have to lift his players as he officially begin his post today ahead of another must-win Europa League clash with Sparta Prague on Thursday.
Goldson conceded his team-mates have “lost a bit of hunger” this season and believes Sunday’s defeat to Hibs indicated a change is required.
He admitted: “We know the new manager was there and you would hope the players would want to impress him.
“But after that performance we need a change. We need a spark. I don’t want to say this but I feel like we’ve lost a bit of hunger.
“All of a sudden we’re champions and don’t need to work as hard - that’s wrong. I feel that’s crept in all season.
“We’ve not been good enough for the whole of this season and hopefully a new manager can come in and give us a spark.”
Despite watching the entire 90 minutes alongside Ibrox sporting director Ross Wilson, Van Bronckhorst opted to remain in his seat as Rangers fell three goals behind.
Ex-midfielder Kevin Thomson insists the former Dutch international should have made his presence felt by taken some form of action.
He stated: “In my opinion, I would have been waiting for them at half-time.
“There was someone (Walter Smith) whose memorial I was at a few days ago and everyone knows how much I think of him, he would have been waiting in the changing room.
“If I was van Bronckhorst I would have been in there waiting for them.”