Dundee United succumbed to fatigue and expectation to cede a two-goal lead against a slick Rapid Vienna side and have their hopes of Conference League progression ripped from their grasp in agonising style in a penalty shootout.

On a febrile night at Tannadice, Jim Goodwin's side went to the well for the sixth time in 22 days and returned with two first-half Max Watters goals, one a cushioned header, the second a pinpoint penalty.

But their dreams of writing a new chapter in the club's storied European history were snatched away in the angst-ridden remainder of this compelling contest.

Rapid, who had looked rattled, rediscovered their shape and ultimately did enough against a patched-up United side who simply ran out of puff against a side who reached the quarter-finals of this competition last season.

Amar Fatah's missed penalty - the first of the shootout - cannoned out off the inside of a post, and he could only watch as the Austrian league leaders scored all five of theirs to advance to a play-off with Hungarian side Gyor.

"As a manager, all you can ask is your team leave everything out on the pitch and we saw that over the last two legs," said Goodwin.

"I've found out a lot about the team, in terms of the characteristics you would want, that never-say-die attitude.

"But to be 2-0 up, to lose in the fashion we did, it's a major disappointment.

In truth, that was the outcome United fans might have feared after Rapid righted themselves and cut their hosts' lead in half just after the hour.

The menacing Janis Antiste - who had spurned a couple of earlier openings - exploited a regular early-season United frailty by heading in from close range, although a United defender might have had the decisive touch.

After that, the wearying Premiership side had to hang on. Ultimately, they couldn't.

Goalkeeper Yevhenii Kucherenko denied Petter Dahl. Ercan Kara was thwarted twice. And any number of shots and crosses were blocked or booted away. But Rapid would not be denied.

Kara flicked in an outrageous leveller and Tannadice deflated. The United players, earlier all vim and vigour, looked leaden.

To freshen things in extra time, Goodwin summoned a teenage striker who spent the second half of last season on loan at Montrose and another youngster who struggled to get off the Falkirk bench.

The former, Owen Stirton, had a dink denied by a fine save but that was as close as United would come in the added half hour.

Instead, they had to rouse themselves once again for penalties.

Fatah's attempt - so close that United fans had to strangle cheers as it flashed back off an upright - proved decisive, though, and ensured that the latest chapter of Tannadice's storied European history comes laced with regret.

Could United go again in this, their sixth game in just over three weeks, with a weary and injury-ravaged squad?

Quietly, many fans would concede that they feared it was beyond their side - and Goodwin himself said Rapid were favourites - but the intensity with which United played belied the effects of these last three weeks.

They hunted down Rapid players, snapped into tackles, and attacked with a fervour that discomfited their feted visitors. Watters goal was the first time United had led in the tie, and his second caused pandemonium.

But Goodwin's side could not maintain that ferocity and Rapid's class would ultimately prove too much.

That United forced it to penalties, having had the better of extra time, is admirable enough but to lose in the manner in which they did will sting.

Zac Sapsford looks a real find. Playing off the left, the Australian was a persistent pest to the Rapid defenders, but allied that to guile and directness.

It was his flick which started the attack for the opener and his burst between two defenders which drew the penalty for the second.

It also caused Sapsford the injury that curtailed his evening at the break. Goodwin will dearly hope it's not too serious, although the forward was spotted with a crutch later on.

Kucherenko was an assured presence in goal; Krisztian Keresztes was a classy performer at the back; and Ivan Dolcek was sorely missed when he went off, too.

And special mention for the three young Scottish substitutes. Stirton, Miller Thomson and Kai Fotheringham could not have poured more into their cameos but, like their more experienced team-mates, they just fell short.

Dundee United manager Jim Goodwin: "I'd like to thank the fans for being with us on the journey and doing the club proud away from home. I'm gutted for every one of them, but grateful to them.

"We've had to ask a lot of the group over the past few weeks. It's my first experience as a manager at this level and it's been so challenging getting the balance right.

"You need to be able to rotate and freshen things. I don't want to use it as an excuse but any team in the country would be suffering without their best players and that's the situation we find ourselves in at the moment."

Former Dundee manager Tony Docherty on Sportsound: "United have taken a real quality Rapid Vienna team to penalties over two legs. The game changed on the introduction of the two substitutes - Kara and Radulovic. They had real quality.

"I'm disappointed for Jim, but he'll take huge pride from that performance. Three of their front four at the end were academy graduates.

"They took it right to the death against a really strong opponent."

Former Dundee United striker Billy Dodds on Sportsound: "United should be so proud. This is a good team they were playing.

"The way they handled it - brilliant first half, near perfection. Rapid got them right back in it, but United got back in the ascendancy.

"Jim Goodwin made the substitutions to make the best chances in injury time and they should have won it then - they had the chances. Rapid never had any."

It's Premier Sports Cup last-16 action for United next, with a trip to Kilmarnock on Sunday (15:00 BST). Goodwin might have a job finding enough fit players.

But a trip to western Hungary to face Gyor with a place in the Conference League proper at stake has eluded them.