Manager Stuart McCall declared himself "relieved and delighted" as Rangers made it through to the play-off final.
He will take on former club Motherwell over two legs for a place in the Premiership after getting past Hibernian 2-1 on aggregate.
"Today was just about character," he said of the 1-0 second-leg defeat at Easter Road.
"We certainly weren't the best team today but we had guts, desire and togetherness and we needed it."
McCall cut an anxious figure on the touchline as Hibs started strongly in the Edinburgh sunshine but the home side lost much of their momentum after 20 minutes.
Rangers, who beat Queen of the South in the quarter-final after finishing third in the Championship, were well-organised and determined, with Hibs unable to find a way past goalkeeper Cammy Bell until Jason Cummings' stoppage-time strike.
"We knew we'd be put under the cosh and a fourth game in 12 days was always going to be difficult," McCall told BBC Scotland.
"But, to a man, we got stuck in and defended well. They all did a shift.
"The fans kept us going for the final 25 minutes because that's all you could hear.
"I was disappointed to lose a goal in the last minute. Thankfully, it wasn't five minutes before because I don't think we could have coped with extra-time; too many tired legs, tired bodies."
McCall's focus now turns to the first leg against Motherwell, the club he left last November after a poor start to the campaign.
"It's great that it's Thursday, it gives us a couple of extra days," he explained.
"The lads have heard two words they haven't heard for a while; 'day-off'. Then we'll look at re-energising.
"I've said before, they've got all of June to be tired. They've got to go again.
"There's nothing to celebrate, we've got two huge games to go."
Asked about facing his former club, McCall replied: "It's not the scenario I would have wanted.
"I thought, with the way Motherwell strengthened in January, they would have enough quality to avoid 11th place [in the Premiership].
"It's a tough one but I'm at Rangers and I'm a Rangers supporter. This is my team, to be honest, and we'll be doing everything in our power to get through.
"We will take confidence from the way we've played. We just need to get the energy levels and the legs back.
"I don't think there were any favourites in our games against Queen of the South and Hibs and I think this will be the same. Nobody will want to call it.
"People might put us as favourites but certainly not me."