Their exit cut off one potential avenue to Champions League football next season and with United four points behind City, who occupy the fourth and final qualifying berth in the Premier League, Van Gaal knows that defeat at the Etihad Stadium on Sunday could be fatal.

“We have to beat Manchester City because that is the other chance to qualify ourselves for the Champions League,” he told his post-match press conference at Old Trafford.

With the FA Cup now the only competition United can win, Van Gaal was asked if failure to overcome Liverpool had increased the pressure on both him and his team.

“The pressure was also today,” the embattled Dutchman replied.

“Manchester United always has pressure. The expectations are always high. The pressure for these players is always very high. We know that and we can cope with that. But we were not lucky today (Thursday).”

Trailing 2-0 after last week’s one-sided first leg at Anfield, United halved Liverpool’s aggregate deficit in the 32nd minute when Anthony Martial lured Nathaniel Clyne into a rash foul and scored the resulting penalty.

But Philippe Coutinho restored Liverpool’s two-goal cushion on the stroke of half-time with a goal that manager Juergen Klopp described as “genius” – the Brazilian leaving Guillermo Varela for dead and then dinking a shot past United goalkeeper David de Gea at his near post.

The game’s closing stages played out to a soundtrack of crowing chants from the away fans, but Van Gaal felt that his team had dominated to the same extent that Liverpool had in the first leg.

“We have played like Liverpool played in the home match with us,” said the United manager, who was presiding over his 150th European game.

“We have done that with them. We have created a lot of chances. We scored a penalty. (Jesse) Lingard, (Juan) Mata, (Marouane) Fellaini, Martial (had chances), and then you concede one goal in the last seconds.

“That’s what we did not do in Liverpool. They scored the away goal and that was the difference.”

He added: “I am not angry, I am not frustrated. I was very proud of my players. They have given everything.

READ MORE: Manchester United and Louis van Gaal ready for Liverpool Europa League reckoning

“I was very pleased the fans also recognised that because they applauded after the match in spite of (the fact) we are out of the Euro League. That was remarkable, I think.”

While Van Gaal braced himself for more inquests about his United stewardship, Klopp remains on course to finish his first season at Liverpool with a trophy in his hands.

“Phil (Coutinho) had a genius moment, wonderful,” beamed the German, whose side will learn their quarter-final opponents in Friday’s draw.

“It was brilliant, what he did. It was the most unexpected thing you could do in a situation like this and it was a perfect goal.”

Klopp, who revealed that skipper Jordan Henderson had vomited at half-time, became the first Liverpool manager to avoid defeat on his first trip to Old Trafford since Graeme Souness in October 1991.

Asked if he would like to face former club Borussia Dortmund – 5-1 aggregate winners against Tottenham Hotspur – in the next round, he smiled.

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“Dortmund, of course not. Why should I want the strongest team in the tournament in the next round?” he said.

“But if we go there, we try to win. I saw only a little bit of the other results, but I’m pretty sure there’s no easy games anymore. It’s not too important. Only we have to be prepared and hopefully we are.”

Dortmund eased through with the prolific Pierre-Emerick Aubameyang scoring twice in their 2-1 win away to Tottenham Hotspur at White Hart Lane that saw them win the tie 5-1 on aggregate.

The Gabon striker lashed a swerving long-range strike past Hugo Lloris on 24 minutes and then added another in the second half to take his tally for the season to 35 goals.

Son Heung-Min pulled one back for Spurs, who are now left to focus on their Premier League title challenge.

Holders Sevilla remain in with a chance of winning the Europa League for the third year running, and fifth time in 11 seasons, after beating Swiss champions Basel 3-0.

After a goalless first leg, Basel were looking to keep alive their hopes of reaching a final that will be played in their own stadium, but Sevilla have a fearsome home record and Adil Rami put them ahead before fellow Frenchman Kevin Gameiro added a quick-fire brace.

Gary Neville’s Valencia were sent crashing out after they lost their last-16 tie to Spanish rivals Athletic Bilbao on away goals despite winning the second leg 2-1.

Valencia had been trailing 1-0 after last week’s first leg at San Mames but looked to have turned the tie around when they went two goals up in the first half at the Mestalla.

Santi Mina got the first goal on the night in the 13th minute, following in to score after Alvaro Negredo’s effort had been saved by Iago Herrerin.

Aderlan Santos then headed home the second eight minutes before the interval, but beaten 2012 finalists Athletic struck the decisive away goal 14 minutes from the end.

The inevitable Aritz Aduriz got the goal, his eighth in nine Europa League games this season, and his 31st altogether, after a superb flick-on by Raul Garcia.

Villarreal are also through after beating Bayer Leverkusen 2-0 on aggregate following a 0-0 draw in the second leg in Germany.

That means three Spanish sides in the last eight, and six left in Europe altogether. In contrast, Italian interest in European competition is at an end after Lazio were humbled 3-0 by Sparta Prague in Rome.

Captain Borek Dockal put Sparta in front and Ladislav Krejci and Lukas Julis added further goals before the break to take the Czech side through 4-1 on aggregate.

The 2009 Uefa Cup winners Shakhtar Donetsk also advanced, Eduardo’s late goal securing a 1-0 win away to Anderlecht in Belgium that took the Ukrainians through 4-1 on aggregate.

The quarter-final line-up was completed by Portuguese side Braga, after the 2011 runners-up overturned a 1-0 first-leg deficit by beating Fenerbahce 4-1 as the Turkish giants ended the game with just eight men.

Ahmed Hassan put Braga ahead only for Alper Potuk to grab an away goal for Fenerbahce.

However, Mehmet Topal was sent off after conceding a penalty that was converted by Josue, and Nikola Stoiljkovic put the hosts ahead in the tie on 74 minutes.

Rafa Silva added another goal for Braga while Fenerbahce also had Potuk and Volkan Sen red-carded.