Juventus' clash with Atletico had originally been set for Tel Aviv but was moved to the Turin giants' training ground on Saturday owing to security concerns following a heightening of conflict in Gaza.
Despite enjoying familiar surroundings, the Serie A club endured a chastening end to their pre-season campaign as Alvaro Morata's treble – as well as a late strike from Matheus Cunha – condemned them to a resounding defeat.
Atletico's win could have been even more comfortable had Joao Felix not seen a first-half penalty saved by Wojciech Szczesny, but Allegri believes Juve will draw valuable lessons from the contest.
"Atletico Madrid is certainly one of the strongest teams in Europe, they have an important squad," he told Sky Sport Italia.
"We arrived a little tired to this match, but even in negative things we must find something positive and in this sense, this match must teach us.
"We only have one week to prepare ourselves in the best way, especially mentally, and to understand that it takes other things to win.
"If we analyse this game and think in a certain way, it will not leave any aftermath. But we know that on August 15 there will be three points up for grabs and the attitude will certainly be different.
"After all, I think it's a defeat that can do us good."
Meanwhile, the Bianconeri boss refused to discuss Morata's future after the former Juventus loanee – who has been linked with a return to Turin – produced a dominant performance.
Morata's future has been subject to debate throughout the transfer window, with Atletico reportedly refusing to sanction another loan move for a player who scored nine Serie A goals and added seven assists for Juventus last season.
Only the since-departed Paulo Dybala (10) outscored the Spaniard among Juve players last term, while no Bianconeri player laid on as many league goals for team-mates.
"I can't say anything about Morata because he is an Atletico player," Allegri added.
"I liked [Gleison] Bremer, even [fellow new signing Federico] Gatti.
"Right now, I have to work with who I have, we have the qualities and the possibilities to start the championship well, but we need to crack down on the attitude and be a little more bad."
Juve begin their Serie A campaign at home to Sassuolo on August 15, with Diego Simeone's Atletico travelling to Getafe on the same day to get their LaLiga season under way.
Thomas Tuchel's side took a deserved lead into half-time thanks to a fine finish from Kai Havertz, who had scored the winner in the Champions League final in May.
Havertz clipped a clever shot high beyond Bernd Leno after being played into space by Timo Werner, who missed a good chance for a second three minutes later.
The Gunners, who brought on new signing Ben White at half-time, drew level 69 minutes in when Granit Xhaka headed in Nicolas Pepe's cross.
However, Chelsea's lead was restored within four minutes as Tammy Abraham slotted a precise finish beneath Leno following a mistake by Hector Bellerin.
Arsenal should have been given an equaliser when Joe Willock crashed a shot off the crossbar and the ball appeared to bounce over the line, but with goal-line technology not in use, it was not awarded.
Mikel Arteta will also be concerned to see midfielder Thomas Partey forced to go off with what appeared to be an ankle injury in the first half.
Chelsea will now face Tottenham on Wednesday before Arsenal take on their north London neighbours on August 8.
Spain and Italy have been two of the hardest-hit European nations during the COVID-19 outbreak, recording 27,709 and 32,007 deaths, respectively.
Everyday life – including sport – has seen massive changes across both countries over the past two months, with lockdown measures only recently beginning to be eased.
The three European giants will play matches next year to determine the winner of the European Solidary Cup, but the main purpose will be to aid the purchasing of healthcare supplies and express gratitude to medical professionals for their work during the pandemic.
The matches will be played across each of the three cities, with the tournament announced for 2021 in the hope fans will once again be able to attend.
A statement released by Los Blancos read: "Real Madrid are set to team up with Bayern Munich and Inter to host the European Solidarity Cup in 2021. The three clubs will come together to send out a message of solidarity and fraternity to the people of Europe.
"The solidarity event will see three football matches held during 2021 in the cities of Madrid, Munich and Milan. The dates for these games will depend on the competitive calendar and of course will take place when the fans are able to return to the stands.
"The three teams will all come up against each other: Madrid vs Inter will happen in Madrid, Inter vs Bayern is set for Milan and Bayern vs Madrid will be held in Munich. The proceeds from these games will go towards the purchase of healthcare resources in Italy and Spain.
"Healthcare staff who continue to fight the pandemic will be represented at all of the games. The three clubs wish to demonstrate to these heroes all of our solidarity, respect and gratitude."
Bayern resumed their 2019-20 Bundesliga campaign on Sunday with a 2-0 win over Union Berlin.
LaLiga and Serie A are not expected to recommence until next month at the earliest, however.
The Premier League clubs and A-League outfit Brisbane Roar were due to play in Queensland in July ahead of the 2020-21 season.
However, those fixtures were unsurprisingly postponed on Wednesday due to COVID-19, which has killed more than 177,000 people worldwide.
"It is a real shame that we will no longer be able to make it over to Queensland this summer, however, it is the right decision to postpone given the circumstances," West Ham manager David Moyes said in a statement.
"The players and I were really looking forward to seeing our fans and the people of Australia, especially as there was great excitement and support for the tournament.
"This is a situation that has affected the entire world, though, and the only thing that matters at this time is that people stay safe and well.
"We hope the tournament can be rearranged at a later date once things are back to normal, and we look forward to visiting Australia in the future."
Australia has seen more than 6,600 coronavirus cases, including 74 deaths.
That is the message from Miami's chief business officer Xavier Asensi, who hinted to Mundo Deportivo that his side will look to make a move for Messi.
Gareth Bale and Giorgio Chiellini made their MLS debuts on Sunday for Los Angeles FC in a 2-1 win over Nashville SC.
Five-time Champions League winner Bale and Chiellini, who won Euro 2020 with Italy last year, joined Wayne Rooney, Zlatan Ibrahimovic and Beckham as some of the biggest names to play in MLS.
With Messi's Paris Saint-Germain contract set to expire at the end of the upcoming season, Asensi suggested Miami will attempt to sign Messi but conceded the aim may be unrealistic.
When asked whether signing a player like Messi was a target for Beckham's side, Asensi said: "Yes, with some caveats. You can't compare Leo Messi with any other player; he's different.
"Having said that, what we're looking for is to be the reference point for football in the U.S., and to do that, the important thing is the players and the show that you can put on.
"To do so, you need the best players, and having them is a genuine objective at this club. In terms of Leo Messi, there's him and then there's everyone else.
"It depends on him and what he wants. We want to have the best players in the world, and I think Messi is the best in history. From there it's up to him."
Messi, 35, experienced a lean first season by his own high standards for PSG, scoring 11 goals in 34 appearances in all competitions.
That return was 17 fewer than he managed for Barcelona in the 2020-21 campaign, his final campaign before ending a 21-year association with the Blaugrana.
Though his goal tally diminished, Messi set up 14 league goals – only once in his last five seasons at Camp Nou (21 in 2019-20) did he assist more in a term.
After making his intentions and admirations for Messi clear, Asensi's focus turned to the pre-season friendly against Barca on Wednesday.
"From an emotional point of view it's marvellous and professionally it's exceptional," he added. "Barca are, if not the biggest, one of the three biggest clubs in the world for sure, and clubs are the ones that capitalise on the passion for football.
"I don't know of any fans of FIFA or UEFA. In international football everyone supports their country, but clubs don't have any borders, they go everywhere. And in terms of clubs, Barca are among the biggest, looking at the numbers.
"Emotionally, it's the biggest thing for me. To have them here, for the people of Miami, is spectacular."
United on Thursday announced that the unnamed players are isolating pending further tests.
A statement on the club's official website said: "Following routine testing of the first-team training group today, we have identified a small number of suspected positive cases.
"This has led to those people isolating, pending further tests.
"As a precautionary measure based on COVID protocols, we have taken the difficult decision that we will not now be able to play the friendly match against Preston North End this Saturday."
The Red Devils were held to a 2-2 draw by Premier League newcomers Brentford on Wednesday, with Anthony Elanga and Andreas Pereira on the scoresheet.
United manager Ole Gunnar Solskajer has expressed his gratitude for the backing he has been given in the transfer market, with Jadon Sancho arriving and Raphael Varane poised to complete his move to Old Trafford.
France centre-back Varane's arrival appears to be imminent, with a deal agreed in principle for a reported £42.7 million fee to secure the Real Madrid man.
Solskjaer's side are due to face Everton in their final pre-season friendly on August 7 and get their Premier League campaign under way a week later against Leeds United.
Mohamed Salah, Sadio Mane and new signing Ibrahima Konate were included in the line-up for the second shortened friendly against the Bundesliga side, while fit-again Trent Alexander-Arnold, Joel Matip and January signing Ben Davies featured for the younger team against Innsbruck.
Alexander-Arnold returned to the playing squad for the first time since suffering a thigh injury on England duty in June against Austria, which subsequently ruled him out of the Three Lions' Euro 2020 campaign that ended in shoot-out heartbreak to Italy.
Divock Origi opened the scoring with a spot-kick in the first game as the Belgian forward profited from a handball that came from full-back Owen Beck's cross.
But Origi's penalty was swiftly cancelled out by Ronivaldo's header past Loris Karius and that meant it was honours even between Jurgen Klopp's men and the Austrian side.
In the follow-up game against Stuttgart, Philipp Forster capped a slick move off to give Pellegrino Matarazzo's men the lead as he finished past Adrian inside the opening 10 minutes.
Liverpool, though, responded through Mane, who squeezed a shot in from close range after Kostas Tsimikas had initially got on the end of James Milner's cross.
And with neither team finding a winner inside 30 minutes, the Reds had to settle for two draws in their two run-outs at their camp in Austria.
Klopp's team next face Mainz on Friday before friendlies against Hertha Berlin, Athletic Bilbao and Osasuna round off their pre-season preparations.
It was 1-0 at the break after Mohamed Salah netted the opener eight minutes into the friendly, with Liverpool making four substitutions before heading back out for the second 45 minutes, including Darwin replacing Roberto Firmino up front.
The former Benfica striker did not have to wait long to get on the scoresheet, stepping up to the penalty spot and converting to make it 2-0 in the 48th minute.
Just three minutes later Darwin was the beneficiary after a turnover deep in the Leipzig defence, getting slipped through on goal by Trent Alexander-Arnold before finishing hard and low across the goalkeeper into the bottom-left corner.
He completed his hat-trick with a lunging tap-in from the edge of the six-yard box, getting on the end of a low cross from Harvey Elliott, before completing his rout with a fourth in stoppage time.
Speaking to the media after the win, Klopp said he was excited to see his side clicking in the second half with their near-£100million man, and that it is the best way to quell any chatter about his hefty purchase price.
"When we struggled a little bit, it was always after three minutes' break we played football again, then a deep breather and play football again," he said. "I wanted us to be a bit more hard with ourselves, go over that point – it's pre-season.
"I think we did that in the second half, obviously. 'Hendo' came on, and [James Milner] – they both were lively.
"Hendo all of a sudden as an eight, went in behind and we created chances. Then Mo gives Darwin the penalty and Darwin – Pandora's box was open. That'a of course a perfect night for him.
"We always think that if you pay a lot of money then the players feel no pressure or whatever – they are all completely normal human beings.
"If the first touch is not perfect then all of a sudden… this generation of players read social media, which is really not smart, but they do. All of a sudden you get in a rush and these kinds of things.
"That's the best way obviously to stop all these discussions. He's a different striker to what we have or what we had, but he's a really good one."
Liverpool's next friendly will take place away against Salzburg next Wednesday.
The Blaugrana ran riot in their traditional Camp Nou curtain-raiser, with goals from Pedri (two), Lewandowski, Ousmane Dembele, Pierre-Emerick Aubameyang and Frenkie de Jong condemning the Mexican side to a crushing loss.
Barca took just 20 minutes to establish a 4-0 lead as Pedri scored twice after laying on new signing Lewandowski's opener, with the Poland striker returning the favour to tee up the skilful midfielder's second strike.
Lewandowski – who scored 50 goals in all competitions during his final season with Bundesliga champions Bayern Munich last term – was named as man of the match, leading Pedri to shower him with praise.
"It was important for us to win in front of our fans and we have achieved it by playing a good game," the midfielder said.
"The coach asks us all to reach the top and that we score goals, and I hope it continues like this. We've had a good pre-season and we wanted to start scoring soon.
"It is a luxury to play with Lewandowski, I really enjoy seeing how he finishes and how he links up.
"The president [Joan Laporta] and everyone have done a great job, and we will fight until May for it to be a very beautiful year for us all."
With Lewandowski joining Franck Kessie, Andreas Christensen, Jules Kounde and Raphinha in moving to Camp Nou ahead of the 2022-23 season, hopes are high that Barca can challenge for silverware – even if speculation persists that they may be unable to register their newcomers.
For Xavi, the performance against Pumas – for whom Barca legend Dani Alves featured – represented the standard the Catalan giants must hit in every match.
"Everything went well tonight, I'm very happy with the good game and for the fans, who have been excited. This is the way," Xavi declared.
"We are in a good dynamic of play and results, but we have to continue working for this to work. The sensations are good, yes, but there is no need to lower the pace or the intensity during the 90 minutes.
"Today it is understood that we relaxed a bit because we were 4-0 very early and it was a friendly, but in official competition you cannot lower your guard."
Barca begin their LaLiga campaign at home to Rayo Vallecano next Saturday.
Widespread reports in Spain said the 42-year-old had been refused the right to enter the US alongside his players because of previous visits to Iran.
Xavi visited the country on AFC Champions League duty during his time with Qatari club Al Sadd, and Mundo Deportivo reported he was not immediately given permission to enter the US as a result.
The United States and Iran have no formal diplomatic relations, and those who have been to Iran may not be immediately eligible to travel to America.
Xavi is expected to be granted permission to travel early next week, reports said.
Barcelona confirmed their 28-player squad left El Prat airport at 14:30 local time on Saturday (13:30 BST), heading for Miami.
They are due to return on July 31 after pre-season games against Inter Miami, Real Madrid, Juventus and New York Red Bulls.
Officials including club president Joan Laporta also made the trip, but Barcelona said in a statement: "Coach Xavi Hernandez will not be taking today's flight for administrative reasons associated to his passport reasons.
"He is expected to join the rest of the squad in Miami in the next few days."
