Xavi believes Barcelona "played with anxiety" at Valencia but "never stopped believing" as Robert Lewandowski struck an injury-time winner at Mestalla.
A tight contest looked to be petering out to a goalless draw when Lewandowski got on the end of a Raphinha cross into the box to divert in a vital goal to bring a smile to Barca after an unhappy few days.
After being eliminated from the Champions League group stage for the second season running prior to losing 3-0 at home to Bayern Munich on Wednesday, the Blaugrana were searching for a morale-boosting win in Valencia.
Speaking after the game, head coach Xavi outlined how much the last week impacted his side's performance, saying: "It was a very important victory. Almost in the last second. We never stopped believing.
"We played with anxiety, the Champions League affected us. Wednesday weighed on us. We suffered. After three quarters [of the game] it became difficult. The decision-making was bad, the result of anxiety.
"We were better than Valencia and we deserved the victory. It wasn't an excellent game, we weren't inspired, but it's vital [the win]."
The 93rd-minute goal from Lewandowski was his 13th of the season, putting him six ahead of his nearest challengers – Real Betis' Borja Iglesias and Espanyol's Joselu (both on seven goals) – in the race for the Pichichi.
"The goal is of quality," Xavi said. "Robert is here to make a difference. I thought it might have been offside, because of the dynamics we had.
"But we have to improve. We have to make better decisions. It could have been a tie and it would be a drama, and it shouldn't be like that. We've improved a lot, we're on the way."
The win puts Barca top of LaLiga ahead of Real Madrid's game at home to Girona on Sunday, but Xavi still believes it is important to put pressure on their great rivals in the race for the title.
"It's very important for the team, we deserved it," he added. "We made an effort, we worked hard and the reward is important. We sleep as leaders, and we want to put pressure on Real Madrid."
Hurtig the hero after late goal sends Arsenal into Champions League quarters
Lina Hurtig's 89th minute winner ensured Arsenal progressed to the quarter-finals of the Women's Champions League after edging Juventus 1-0 on Thursday.
After being frustrated for large parts of the encounter, Hurtig bundled home from close range after Martina Lenzini's poor clearance to book the Gunners' place in the last eight.
Despite Arsenal dominating the early exchanges, it was Juventus who had the first sight of goal, though Eva Schatzer's effort was easy for Daphne van Domselaar to gather.
In a first half that saw just two shots on target, both coming from the visitors, Renee Slegers' substitutes proved to be the difference for Arsenal.
Slegers introduced Beth Mead, Stina Blackstenius and Hurtig late on, with the latter somehow putting Kim Little's cross over the bar from five yards out.
However, the Swede would atone for her earlier error, combining with fellow substitute Blackstenius to net against her former club and send them out of the competition with two group games remaining.
Meanwhile, in Group D, Barcelona edged closer to the quarter-finals of the competition with a convincing 4-1 victory over St. Polten at the Generali Arena.
The reigning champions are still three points behind Manchester City following their 2-1 win over Hammarby, and know a win against the Swedes next month will see them progress.
Kika Nazareth opened the scoring in the 20th minute after capitalising on a mistake by Kamila Dubcova, notching her second nine minutes later from close range.
Barca found themselves three goals up at the break when Vicky Lopez netted her first goal in the competition to put the result beyond doubt.
There was also a landmark moment for Alexia Putellas, who netted her 200th goal for the club with a well-taken effort into the far corner.
Valentina Madl took some of the shine off an otherwise impressive display from the visitors, who have now taken their tally to 20 goals from their four matches in the competition.
Guardiola agrees two-year contract extension with Man City
Pep Guardiola will be Manchester City manager for at least two more seasons after 2024-25, after he signed a two-year contract extension on Thursday.
The 53-year-old was coming to the end of his City deal, which was due to expire at the end of the current campaign, but he has opted to remain at the Etihad Stadium.
The deal itself will take Guardiola's tenure at the club to over a decade, making him City's longest-serving manager since Les McDowall in 1963.
There had been suggestions that he may leave at the end of the season following the announcement that director of football Txiki Begiristain was on his way out.
Guardiola was strongly linked with the England job after Gareth Southgate resigned in the wake of their Euro 2024 final defeat, but the Football Association appointed Thomas Tuchel last month.
“Manchester City means so much to me," Guardiola said. “This is my ninth season here; we have experienced so many amazing times together. I have a really special feeling for this football club.
“That is why I am so happy to be staying for another two more seasons.
“Thank you to everyone for continuing to trust and support me – The Owner, The Chairman Khaldoon, Ferran, Txiki, the players and, of course, the fans… everyone connected to Manchester City. It has always been an honour, a pleasure and a privilege to be here.
“I have said this many times before, but I have everything a manager could ever wish for, and I appreciate that so much.
“Hopefully, now we can add more trophies to the ones we have already won. That will be my focus.”
Having been appointed in 2016, Guardiola is by some distance Manchester City's most successful manager of all time, having won 18 major trophies during his time at the club.
That list includes their first-ever Champions League triumph in 2023 and six Premier League titles, including an unprecedented four on the spin.
He also boasts a 72.04% win percentage across all competitions, which is unsurprisingly the highest of any full-time City manager in history.
Shaw at the double as Man City progress in Champions League
Khadija Shaw scored twice as Manchester City beat Hammarby 2-1 to seal their place in the Women's Champions League quarter-finals.
Gareth Taylor's team entered Thursday's game with a perfect record in Group D, and their fourth win in as many European matches ensured they finished in the top two.
Shaw—the leading scorer in the Women's Super League this season with eight goals—put them ahead in the 31st minute, driving into the area after taking in Yui Hasegawa's pass before seeing her shot deflect into the top corner.
Shaw was booked for celebrating in front of the home fans despite appearing to have objects thrown at her from the stands, and Hammarby should have levelled when Julia Blakstad fired wide 10 minutes later.
The hosts did draw level three minutes into the second half as Ellen Wangerheim tapped home while City's Laura Blindkilde Brown was down appealing for a free-kick.
That parity was short-lived, though, as Shaw blasted into the top corner from 25 yards out, taking her overall tally for this season to 12 goals in all competitions.
In Group C, meanwhile, Bayern Munich lost their perfect record as they played out a 1-1 draw with Valerenga, boosting Arsenal's hopes of topping the pile.
Jovana Damnjanovic came off the bench to put Bayern ahead 15 minutes from time in Norway, but Elise Thorsnes headed home following an 88th-minute corner to snatch a point for the hosts.
Arsenal could now move within a point of Bayern when they face Juventus in Group C's other match later on Thursday.
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