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."
Barcelona boss Flick calls for LaLiga suspension after Spanish floods
Barcelona are in high spirits ahead of Sunday's derby against Espanyol, though Hansi Flick does not think LaLiga matches should be played this weekend.
Barca thrashed Real Madrid 4-0 at the Santiago Bernabeu last weekend to establish a six-point lead in LaLiga but their city rivals Espanyol are 20 points behind and languishing in 17th place, a point above the relegation zone.
Yet Flick feels it is wrong that LaLiga is playing on in the wake of the flash floods that have devastated regions of eastern Spain, with Valencia particularly impacted.
Madrid's game against Valencia was naturally postponed, but most other fixtures in Spain's top tier are going ahead.
"If it were me, I might [suspend LaLiga] because it is an incredible tragedy for Valencia and Spain as a whole," Flick said.
"We have spoken with Ferran [Torres] who is from the area, and it is not easy to decide whether the game should be played or not.
"It is a tragedy. It was something similar in Germany three years ago, it is horrible. We will do everything we can to help. The rest is for LaLiga to decide."
Barca do hold a brilliant record against Espanyol, having not lost in their last 26 encounters with their city rivals.
Flick, though, warned his side against any complacency.
"I know what a Barca-Espanyol derby means. It will be a tough match, for sure. After a fantastic week, it is important to be at 100% tomorrow, with intensity and maximum quality," Flick said.
"We always prepare well for the next game. After the celebrations, we focus on the next game. We work on what we want tomorrow. It's a very long game in the league and we focus on the next game."
Barca have taken 30 points from their first 11 league matches this season, their second-highest tally at this stage of a campaign in the competition, after 31 points in the 2012-13, 2013-14 and 2017-18 seasons.
Simeone: It makes no sense to play after Spanish floods
Atletico Madrid coach Diego Simeone is unhappy that most LaLiga matches will go ahead this weekend after catastrophic floods swept the eastern region of Spain.
The deadliest flash floods in Spain's modern history have killed over 200 people and dozens were still unaccounted for, four days after torrential rains swept the region of Valencia.
The tragedy is already Europe's worst flood-related disaster since 1967 when at least 500 people died in Portugal.
Saturday's clash between Valencia and Real Madrid, as well as Villarreal against Rayo Vallecano, are among several games postponed over the weekend after the floods.
"It doesn't make any sense," Simeone told reporters ahead of his side's home game against Las Palmas on Sunday.
"What is happening is very hard; it is very moving to see the people who went out on the streets to help, who with a shovel and their tools are trying to collaborate and that speaks very well of the country, of the people, and we want to help wherever we can.
"There are people having a very hard time, it's very sad and they tell us to continue and here we are, continuing."
Last month, Las Palmas named former Espanyol boss Diego Martinez as their new coach, and while Simeone is not pleased that the game is going ahead, he is prepared for a tough encounter.
"We have a tough game against a team that has improved a lot since the arrival of the coach," Simeone said.
"They are more forceful and I imagine a dangerous game, with a lot of counter-attacking, fast people in attack and we will try to have a game with these situations under control and get it out with the help of our fans, which is always fundamental."
Arsenal deserved to lose against Newcastle, says Arteta
Mikel Arteta was left frustrated by Arsenal's performance in their 1-0 defeat away to Newcastle United on Saturday.
The defeat left them third in the Premier League, though they could be up to eight points behind Manchester City by the end of the day.
Arsenal had 63.9% possession and mustered more shots (10) and a higher expected goals total (1.11) than Newcastle, but could not find a leveller following Alexander Isak's early header.
And Arteta was disappointed with how his side did the basics following what he thought was a good start.
"We deserved to lose today. I thought we started really well and were really dominant. We didn't defend the box well enough," he told Premier League Productions.
"Credit to them. They scored a great goal with a good ball.
"Then the game changes and you start to play a different game. You have to adapt and we didn't do that well enough. I am very frustrated.
"We got dragged into a game they are looking for constantly and we couldn't play the game that we wanted."
Arsenal only managed one shot on target in the match, coming from a Mikel Merino effort that was cleared off the line in the first half. Declan Rice, meanwhile, put a close-range header wide in second-half stoppage time.
"We had two big chances: Mikel had a big one, Declan had a big one. We lacked answers," said Arteta.
Newcastle boss Eddie Howe, meanwhile, was delighted with the Magpies' performance as they sealed back-to-back victories following their win over Chelsea in the EFL Cup on Wednesday.
"You have to be really strong mentality and know results will turn if you continue to do the right things," Howe told BBC Sport.
"It has been a difficult week with the fixtures, but the players have done really well.
"There was a better feeling in training after the Chelsea win, as if pressure lifted slightly.
"Today's performance was built on hard work, desire and a lot of really good defending in the second half. I thought we looked good."
Isak headed home from a pinpoint Anthony Gordon cross to tally up his third goal in three successive appearances in all competitions.
"I wouldn't say it is a trademark goal for Alex but really pleased to see it. Anthony can give you that on his natural right-hand side and it was a great ball," said Howe.
"It was always going to take a moment like that as it was a game of few chances."
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