Nico Williams' late goal finally ended Rangers' Europa League dreams as Athletic Bilbao reached the semi-finals to maintain their hopes of winning the tournament on home soil.

After battling to a goalless draw at Ibrox despite playing most of the first leg with 10 men, Rangers needed a near-perfect performance against La Liga's fourth-place side, and were still in the tie with 11 minutes left.

However, Spain international Williams headed home Oscar De Marcos' beautiful cross to kill Rangers' chances of a second final in four seasons, after Oihan Sancet's penalty in first-half stoppage time broke the deadlock.

Conceding the first goal at that point was a cruel blow for Barry Ferguson's side, but in truth it was no less than Athletic deserved for their first-half dominance.

It was John Souttar who was penalised for running into Maroan Sannadi just as the interval approached, but Rangers did at least respond positively for a spell after the break.

Not helped by injuries to defenders Ridvan Yilmaz and Leon Balogun, they kept the ball better and went agonisingly close to an equaliser when Nicolas Raskin's close-range shot was touched on to a post by goalkeeper Julen Agirrezabala.

There will be plenty of wistful thoughts about that chance, as there will be for a controversial moment when the game was goalless.

Cyriel Dessers was pulled back in the box by Dani Vivian to the extent his shirt was ripped, but the officials deemed the contact as fleeting and there was no Rangers penalty or red card.

But apart from that nervy moment and Raskin's close shave, Athletic were fairly comfortable in defence, as their dream of winning the Europa League at their San Mames home moves a step closer.

There was always a sense this tie would be a bridge too far for Rangers. Athletic are flying high in La Liga and on a mission to win this tournament.

However, the Ibrox side have had a habit of performing near miracles on the Europa League stage, consistently defying the odds.

But when Dessers' ripped shirt only lead to a yellow card for the Nigerian for dissent rather than a penalty, you got the sense there would be no luck on their side.

Injuries to Yilmaz, Ianis Hagi, and Balogun forced Ferguson and his staff into multiple changes of shape as they tried to adjust.

But luck and injuries aside, Rangers were also outclassed over the tie.

Athletic, channelling the energy of a fervent crowd, hounded them out of possession and piled the pressure on in the first half.

Rangers went close to holding out until half-time, but Souttar's foul robbed them of the chance to regroup with the game goalless.

A brief flurry after the break and the fact their hosts had only found one goal kept hope flickering, but Athletic have the best defensive record in La Liga and largely held them at arms' length until Williams pounced to extinguish it.

Rangers can be proud of another good run at this level, but their season is now over and the questions will start about an uncertain future.

When will the takeover by the San Francisco 49ers group be completed? Who will the manager be? How many players will leave?

These are the only questions left for the club to focus on after a trophy-less season.

Athletic, a club who only play Basque players, are built on emotion and identity.

A chance to win a Europa League at San Mames is once in a lifetime for these players and their fans, and this squad appear to be carrying that pressure lightly.

Experienced coach Ernesto Valverde is a calming influence and has this side playing disciplined but exciting football, with their first-half pressing particularly impressive.

While in the second half they kept calm when Rangers had their moments to get the job done with a bit to spare.

In Spain's European Championship winner Nico Williams they also have a star who will cause Manchester United problems in the semi-finals as they aim to reach a first final since 2012 when Marcelo Bielsa guided them to the showpiece.

Rangers interim head coach Barry Ferguson: "Obviously disappointed. The work rate was there but the quality wasn't.

"[We should have had] two penalties. It's a clear pull on Cyriel [Dessers], it's a clear red card. In the second half with Nicolas [Raskin], it strikes [the defender's] hand and that's another penalty.

"At the end of the day, we were up against a quality team. Sometimes you have to hold your hands up.

"It's going to hurt. We need to go away and reflect a bit before finishing the season as strongly as possible."

Rangers striker Cyriel Dessers: "Ball gets deflected into the box, I think I can get to it, then my shirt gets pulled.

"Even if there's doubt, you can look at the shirt. It's not possible in he middle of the pitch, it's not possible in the box.

"We're on the wrong side of it today. It hurts."