Stand-in skipper Jonny Hayes has demanded Aberdeen did deep and show their character to close out a third-placed finish.
Finishing third will earn European group stage action until December and a UEFA prize payment of around £3 million – if Celtic win the Scottish Cup.
Aberdeen currently occupy this golden third spot, five points clear of fourth-placed Hearts with four games remaining.
Pushing to finish third was inconceivable in January when the Reds were in the bottom six after a crash in form which saw boss Jim Goodwin sacked.
Under the guidance of Barry Robson, Aberdeen have turned around a troubled season.
A winning streak which extended seven games ended with a 1-0 loss at Rangers on Sunday.
Hayes has urged the Dons to bounce back from that Ibrox loss to close out the race to finish third.
He said: “Now we are fighting at the right end of the table, it is about showing that character, leadership and mentality to stay there.
“The expectation of the fans is that they want Aberdeen up at the top end of the table.
“I am always trying to get us as high up the table as possible as well.
“And for a club like Aberdeen we are always looking forward.
“This season we just didn’t play well enough in that period after the winter break, it was not lack of effort.
“The response since then to go on a run and pick up a good amount of points shows good character and good leaders in the squad.
“You have got to have that resilience to pick yourself up.”
No hangover from Rangers defeat
Despite defeat at Ibrox, the Dons did not lose any ground in the race for third as Hearts went down 2-0 to Premiership champions Celtic.
Hayes insists there will be no hangover from the loss in Glasgow as the Dons’ longest winning run since 2015 ended.
All focus quickly switched to hosting Hibs on Saturday.
He said: “The manager has had that mantra of one game at a time.
“Regardless of how we have got on in previous fixtures, it is always a case of coming in on Monday morning and resetting.
“Now it is about resetting and working towards the next game.
“That is the way we have worked over the last number of months and nothing will change.”
You must take your chances at Ibrox
Hayes skippered the Dons at Ibrox because captain Graeme Shinnie and vice-captain Ross McCrorie were both ruled out.
Shinnie was serving the second game of a four-match ban while McCrorie recently underwent hernia surgery.
Aberdeen were gunning for back-to-back victories against Rangers having recently beaten the Ibrox club 2-0 in the Granite City.
Striker Duk, who has netted 18 goals this season, missed two clear scoring opportunities in the first half at 0-0.
Hayes said: “Unfortunately we didn’t take them.
“It is all part of a learning curve.
“Some of the guys need to realise when you go to a place like Ibrox you need to take your chance to take something from the game.
“In saying that I won’t be overly critical of Duk as he has bailed us out on numerous occasions this season.
“As a team when you put yourself in those positions you have to take them.
“Regardless of the opposition we want to win games and do our best to win.
“I thought we defended excellently and it is a wonder-strike from a set-piece that beat us.”
Boss Robson’s Ibrox game-plan
Aberdeen’s impressive clean sheet run finally ended when Todd Cantwell volleyed home the winner for Rangers in the 64th minute.
The Dons had registered five successive clean sheets prior to facing Rangers in Glasgow.
Hayes insists boss Robson’s game-plan was working at Ibrox – which is why conceding at a set-piece is so frustrating.
He said: “There are different ways of playing games, sometimes you have to set up differently tactically.
“You are not coming here (Ibrox) to defend for 90 minutes.
“The game-plan from us, regardless of how it looks from the outside, is to always try and win the game.
“Sometimes it is to sit off for long periods, sometimes it is to try and attack and press high up the pitch.
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“The manager, since he has come in, has been spot on in his preparation.
“Our game-plan was to press at the right times.
“We worked on them building in a three or a four and we were prepared for it.
“We knew it was not always going to work, that is the risk of trying to press them high.
“Our game-plan, bar that 10-minute spell when we were five yards too deep, was pretty spot on – so we were disappointed not to come away with anything.”
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