The Light Blues have fallen behind Aberdeen in the race for second spot in recent weeks after a run of one victory in seven Ladbrokes Premiership matches.
Some within the Rangers squad were open in their aim of launching a title challenge ahead of this season but Celtic’s form quickly ensured that was a pipe dream.
Rangers chairman Dave King subsequently explicitly stated that a “strong second” had been the realistic expectation and failure to consolidate that was one of the reasons Mark Warburton departed as manager.
But third place would guarantee entry to the Europa League first qualifying round, just the same as the William Hill Scottish Cup winners and league runners-up.
And Hill claims the exit of the manager, on top of the challenges in building the club up since 2012, means that would constitute success.
“With the current situation the club is in, and the situation it has been in for the last five years, then I think it would be, yes, unfortunately,” said Hill, who has recovered from a head injury ahead of Wednesday’s visit of St Johnstone.
“This club is built on success and winning things, and in any other circumstance being third is not a success.
“But at the moment, where the club is, and the difficulties they have been in, I think getting a European spot would be counted as a success.
“It was always European qualification that was one of the objectives this season.
“Unfortunately we have let Aberdeen slip away from us a little bit. It’s still not over by any means. We still have to play them twice.
“But European qualification was one of the main aims and objectives this season.”
Rangers have suffered league defeats to Dundee and Inverness under caretaker manager Graeme Murty and Hill believes securing a new boss would help ward off any threat of them falling outside the top three. St Johnstone could cut their deficit on Rangers to three points at Ibrox.
“It’s always at risk,” Hill said. “Every game you go into there is a chance of teams picking up points against you. Unfortunately it’s getting a lot tighter now with the last two results we’ve had.
“Obviously getting someone in, the sooner the better, would be great for us.
“But European qualification is still something that we want, still something that we hold in our hands, so we have to react to the two disappointing results that we have had.”
Despite his wish for the managerial situation to be sorted out, Hill stressed that the players should take responsibility for their form.
“I don’t think it’s rudderless,” the 38-year-old said. “As players you are professionals and you’ve got a duty to go out and perform.
“I think it’s important as a professional, and I’ve been in this game long enough, you have got to ignore all the noise that’s outside these four walls.
“There’s going to be a lot of people that are going to criticise you, be against you and enjoy us going through a difficult patch. We have got to ignore all that noise and just concentrate on this team.
“I’m not on Twitter, I don’t watch the news or anything like that, so whatever you write about me doesn’t even bother me.”