Unai Simon acknowledged Spain would have to recover their focus amid celebrations of a quarter-final win over Germany that felt "like a Euros final".
La Roja are still two victories from the Euro 2024 title, but they have cleared their greatest hurdle yet after beating the hosts 2-1 late in extra time on Friday.
Subsitute Mikel Merino headed a 119th-minute winner, with Spain earlier frustrated by a Florian Wirtz equaliser at the end of normal time.
Goalkeeper Simon was in no mood to talk down his side's achievement, even if attention must soon turn to Tuesday's semi-final.
"What we have achieved is historic, winning this game is like a Euros final," he said.
"We have already celebrated, but we have to recover because in four days we have a semi-final."
Spain and Germany had perhaps been the tournament's two standout teams through the first four rounds of matches, and this meeting did not disappoint.
"It was the match we were all waiting for, between two of the best teams in the world," said Merino.
"It could be a World Cup final or a European Championship final; the level of those who have come off the bench is very high.
"We have shown that we know how to suffer, that we have a great team."
Spain suffered physically as well as mentally in a feisty encounter that saw 15 cards – the second-most in a Euros match – even if they gave as good as they got.
Robin Le Normand's second yellow card of the finals will now see him miss the next round, with Dani Carvajal also banned. He was already set to sit out the semi-final even before a last-gasp second booking – and third of the tournament – saw him sent off.
Alvaro Morata also appeared to be suspended for a card from the bench in the aftermath of Merino's goal, but the caution was later removed by UEFA.
Regardless, Spain coach Luis de la Fuente is backing the players on the fringes of his squad to deputise in the same effective fashion as super sub Merino.
"Any of the 26 players are ready," he said. "Each one has his role at the right time.
"I am very proud of these players. Tomorrow we will recover, and we will try to have as many players as possible."
De la Fuente might also be without Pedri through injury following a foul from Toni Kroos that was not punished with a card.
The Barcelona midfielder was wiped out in the opening minute of the match and soon had to be replaced by Dani Olmo, who himself stepped up with the opening goal and an assist for Merino.
"Pedri was in pain," De la Fuerte said. "I think it was a red card [for Kroos].
"Whether Pedri is on the pitch or off [for the rest of the tournament], he's going to keep contributing."
However, the coach added of Germany's rugged approach: "These are games like that, when you're playing for so much, at this stage, you have to use all your weapons. I have no complaints about German football."
Arsenal 'always find a way' – Arteta
Mikel Arteta showered praise on his Arsenal players after their 3-1 victory against Southampton, saying his squad will "always find a way" to win.
The Gunners bounced back from Cameron Archer's opener to earn their 400th Premier League home win on Saturday, with Kai Havertz, Gabriel Martinelli and Bukayo Saka on target.
Arsenal enter the international break in third, hot on the heels of leaders Liverpool and level on points with Manchester City.
They also continued their impressive record against Southampton, extending their unbeaten run against them in the top flight to 25 matches (W17 D8), but the hosts were made to work for the win.
Arteta's side registered 14 shots in the first half with an expected goals (xG) total of 1.15, though their only shot on target came in stoppage time courtesy of Thomas Partey.
The introduction of Martinelli, Leandro Trossard and Mikel Merino prompted an improvement in attack shortly after Havertz's leveller.
"The start was exceptional, the dominance, the chances. It was unbelievable not to go one, two, three goals up," Arteta said.
"We conceded the goal, and then it was game on.
"I thought the team reacted with a lot of authority, and I am happy the team can react like this - but not happy after the chances we had that we had to go through that.
"The substitutes changed the energy and also the feel in the crowd. We won in the end and I think we deserved it. This team always finds a way.
"The way we started was phenomenal, but we didn't get our reward. We had a difficult context at 1-0 but we did it."
Arteta also lauded Saka's performance after the England international took his goal involvement tally to nine for the season with his strike coming after two assists.
This campaign, only Erling Haaland and Cole Palmer (10 each) have been involved in more goals than Saka.
The 23-year-old has also taken on the role of captain in Martin Odegaard's absence, something Arteta believes Saka is embracing.
"For sure. That's the maturity and steps players have to do. He's been in the team long enough to earn the right to have that role. He believes in that," Arteta said.
"He has the capacity to change and decide games like many other players. If we want to be at the top, sometimes players have to create those moments, and he's certainly done that again today."
Southampton, meanwhile, are now without a win in their last 20 Premier League matches, equalling their longest top-flight winless run (a run of 20 between August and December in 1969).
But they had their moments to level the contest, with Tyler Dibling's deflected effort and Taylor Harwood-Bellis' header striking the woodwork prior to Saka's settler.
"I feel so much more positive and proud of my team than I did on Monday [after a 3-0 defeat at Bournemouth], and we played against one of the best teams in the country," Russell Martin told BBC Sport.
"If we play like that in the next block of games, I'd be very happy. I think we're learning and growing, and we're on a journey. But we're doing it under huge scrutiny and the intensity of the Premier League.
"I have to keep the guys on track and on path. There's a lot to be frustrated about, we don't have enough points on the board and a win yet, but I loved all of our resilience."
Lopetegui praises West Ham's 'strong mentality' after first home win
Julen Lopetegui had plenty of praise for West Ham's "strong mentality" as his side triumphed 4-1 against Ipswich Town at London Stadium.
It marked the Hammers’ first win at home this Premier League season, while Ipswich remain winless.
The hosts went 1-0 ahead after 48 seconds through Michail Antonio - West Ham’s earliest Premier League goal on record.
Having been pegged back to level terms just five minutes later when Liam Delap scored following a corner, Lopetegui was pleased with how his side set about regaining control, with Mohammed Kudus, Jarrod Bowen and Lucas Paqueta on target.
"We started better but we suffered a very early goal too. We conceded from the first corner and maybe we could have done better. It was key as the team then showed a strong mentality," he said, as quoted by Sky Sports.
"In the bad moments, you have to be strong. We did against Brentford and we did again today. It's important to highlight as it will help us become a better team."
West Ham proved the dominant force, registering 23 shots with 17 of them coming from inside the box. It meant Lopetegui’s men accumulated an expected goals (xG) total of 3.17 by full-time.
"We're happy when we win. We work for this. We're happy for the fans as they deserve this and for the players as they are working very hard. It was against a good team. They didn't lose to Villa, Fulham, Southampton, Brighton so it's a good win,” he added.
For Lopetegui's counterpart Kieran McKenna, the result was another stark reminder of the challenges the Premier League presents for a promoted side.
The Tractor Boys sit in seventeenth, just one point above the relegation zone.
"It ended up a disappointing day for us. There was a large majority of the first half in which it was a competitive game that was evenly fought. We played some good football but we conceded poor goals which changed the momentum of the game," McKenna said.
"We didn't deal well enough with the direct play. The goals came from those moments so there's a lot for us to learn."
Ipswich allowed their opponents 28 touches inside their box, while they were reliant on the woodwork to stop West Ham from adding to their lead.
"They didn't have to work hard for their goals. Apart from the fourth, the goals came too easily. They have quality and they showed that with the goals and chances they created if you give them opportunities," reflected McKenna.
Championship: Sheff Utd joint-top after win over Luton, Rooney sent off but Plymouth prevail
Sheffield United maintained their unbeaten start in the Championship and moved joint-top of the table with a 2-0 home win over Luton Town.
Jesurun Rak-Sakyi marked his 22nd birthday in style, scoring a goal in each half, as the Blades brushed aside their struggling visitors on Saturday.
The youngster was denied in the opening stages, but still ensured United got off to a strong start, firing in an emphatic finish after just 12 minutes.
He then got his second just seven minutes after the restart, sliding it through Thomas Kaminski's legs.
The Blades should have had a third late on when Vinicius Souza struck the post, but they had already done enough to take advantage of Sunderland dropping points on Friday to join them on 19 points at the summit.
Luton, meanwhile, are winless in three as they sit just above the relegation zone in 21st place.
Elsewhere, Plymouth Argyle snatched a dramatic 2-1 home win over Blackburn Rovers, after manager Wayne Rooney had been sent off.
Michael Obafemi's 15th-minute goal looked enough to secure a win until Joe Rankin-Costello equalised with four minutes left of normal time.
Rooney was subsequently sent to the stands for his protests as he felt there was a foul in the build-up, meaning he was not on the touchline when Morgan Whittaker headed in a last-gasp winner in the seventh minute of stoppage time.
Watford also secured a late victory, with Tom Cleverley's side coming from behind to beat Middlesbrough 2-1 at Vicarage Road.
It initially looked like they were in danger of falling to a second consecutive defeat, having failed to create chances before George Edmundson took advantage of slack defending to put Boro ahead.
However, the Hornets' substitutions swung the game back in their favour, with Edo Kayembe pulling them level before Kwadwo Baah's half-volley secured the points in the 87th minute.
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