Juventus suffered a humiliating 2-0 defeat at Maccabi Haifa on Tuesday, leaving Allegri's team on the brink of a group-stage exit from the Champions League.
Meanwhile, Juve have taken just 13 points from their first nine matches of the Serie A season, their worst return at this stage of a campaign since 2015-16 (12), and are already 10 points adrift of leaders Napoli.
Bianconeri chairman Andrea Agnelli was forced to reject reports Allegri would be fired following the loss in Israel, after which the Juventus coach revealed the team would hunker down at their Continassa training ground ahead of Saturday's Derby della Mole.
Subsequent reports suggested that decision irritated several players, but Allegri claimed that is not the case on Friday, saying: "These are unfounded rumours. The team has never asked not to retire.
"We know the moment, we came back on Wednesday, we trained when we arrived and the next morning we were on the pitch.
"We are focused on trying to get out of this situation which is certainly not beautiful. We know that we cannot come out with just one match, but we must start achieving results.
"I talk to the team every day. Withdrawal is just a moment to be together, it is not a punishment.
"We had yesterday and today to do double workouts, to give a little more order because it is normal that when there are no results, we tend to see things blacker than they are."
Juventus are winless in their last six away games in Serie A (D2 L4), their longest such run since they failed to win on seven consecutive road trips in 2010, but Allegri says the Bianconeri retain a sense of togetherness.
"It is not my personal challenge, it belongs to everyone," he added. "It is not that one wins and the others lose, it is done all together.
"The team has worked well for two days, this afternoon we will do the last refinement and then we will arrive tomorrow evening to play against Torino."
Conte and Agnelli clashed on Tuesday during the second leg of the Coppa Italia semi-final in Turin, a match that ended 0-0 to see Juve prevail 2-1 on aggregate.
Footage appeared to show the ex-Juve boss making a gesture that was reportedly towards Agnelli, who could be heard on a pitch-side microphone making comments aimed at the touchline following the end of the game.
Speaking to RAI after the draw, Conte said Juventus should "tell the truth" over what unfolded, adding: "They should be more polite in my opinion. They need more sportsmanship and respect for those who work."
Juventus defender Bonucci understands that while those involved in top-level football must set an example to the audience watching on, it is not always easy to stay calm in such high-pressure situations.
"There is little to add, the images speak clearly," Bonucci said in an interview with Sky Sport Italia. "What happened is bad, but it is not up to me to judge why it happened or what had to be done.
"Obviously we must always be an example, but sometimes it is difficult. When you step onto the pitch the environmental situation does not make you think.
"In some moments, adrenaline and tension make you become something different than what you would like to be, episodes like this happen, amplified by the empty stage with the sideline microphones that can transmit a sneeze."
Juve had won the first leg 2-1 at San Siro, having previously lost 2-0 at the same venue in January when going up against the Nerazzurri in Serie A action.
Bonucci points to that league defeat as a turning point for the reigning champions of Italy, as Juventus have not lost in seven games since that setback. Their reward for progressing in the Coppa Italia is a final showdown with Atalanta, which takes place in May.
"It represents a small step towards another goal, which is to bring home the trophy. It will be difficult, because Atalanta have been one of the best Italian teams for several years, they have also shown it in Europe," the defender said.
"It will be an unprecedented and complicated final, but there will be the desire to take home the cup.
"For the group it is yet another confirmation that after the match in Milan with Inter something different has taken place in us as a team and as individuals and this bodes well."
Juve switch their focus back to Serie A this weekend, though Bonucci is an injury doubt for Saturday's game away at Napoli due to a muscle issue.
Midfielder Arthur also appears set to miss the fixture after the club revealed he has "the presence of a post-traumatic calcification at the level of the interosseous membrane" in his right leg. The Brazilian will be monitored on a daily basis, though it is unclear when he will return to action.
The proposed Super League was announced on April 18th last year, although nine of the competitions' 12 founding clubs moved to renounce the idea within days after it provoked a fierce backlash from across the footballing world.
However, Madrid, Barca and Juve remain committed to the project, with Bianconeri president Andrea Agnelli reportedly keen to kick-start a new proposal.
Speaking at the Financial Times' Business of Football Summit in London, at which Agnelli was present, the UEFA president has now hit out at the clubs' owners for discussing the return of the controversial competition during the midst of Russia's invasion of Ukraine.
"First they launched [this] nonsense idea in middle of a pandemic," Ceferin said of the club owners. "Now we are hearing they are launching another in a war.
"They must live in a parallel world."
Ceferin has previously labelled Agnelli, as well as the Spanish giants' presidents Florentino Perez and Joan Laporta, as "incompetent", and accused them of trying to "kill football".
Meanwhile, Ceferin also spoke about the sporting sanctions being placed on Russia in the aftermath of the invasion on Ukraine.
FIFA and UEFA have moved to expel Russian teams from its competitions, including the upcoming Women's European Championships in England, for which Russia had qualified, while St Petersburg has been stripped of this season's Champions League final.
The Bianconeri will see a major shakeup in management after confirmation that a shareholders' meeting scheduled for last week has been postponed to next month.
Alongside Agnelli, who has been in charge of the club since 2010, vice-president Pavel Nedved and managing director Maurizio Arrivabene are also among those who have quit.
Arrivabene will apparently remain as the club's chief executive officer to oversee the introduction of a new board, which will be confirmed in January.
In a statement from the club, Juventus confirmed the board's decision to resign had come in the wake of advice following issues raised by Consob, the Italian securities market government authority, and auditor Deloitte.
"The members of the Board of Directors, considering the centrality and relevance of the pending legal and technical-accounting issues, have deemed it in the best social interest to recommend that Juventus adopt a new Board of Directors to address these issues," it read.
"To this end, on the proposal of the chairman Andrea Agnelli... all the members of the Board of Directors present at the meeting declared that they resigned from their office.
"The Board has requested Maurizio Arrivabene to maintain the position of Chief Executive Officer."
The announcement seemingly ends a decades-long relationship with the club for Agnelli, who was the fourth member of his family to serve as chairman.
Juventus are currently third in Serie A, but missed out on progressing to the knockout round of the Champions League, instead dropping into the Europa League this season.
Paris Saint-Germain – for whom Al-Khelaifi is chairman and chief executive – were, along with Bayern Munich, one of the few heavyweight European clubs to elect against joining the planned breakaway competition, which collapsed before it ever got started.
Only Real Madrid and Barcelona are yet to confirm their withdrawal from the now-suspended tournament, after all six English teams involved pulled out on Tuesday, with Atletico Madrid, Juventus, Inter and Milan following suit on Wednesday.
During a remarkable situation which rolled out over Sunday and Monday, Juve chief Agnelli – a major driving force behind the proposals – resigned from his post as the ECA chairman.
With PSG having rebuffed the invitation to join the European Super League, Al-Khelaifi issued a strong statement condemning the actions of the 12 clubs and backing UEFA.
Al-Khelaifi, who has been in charge of PSG since 2011, has now been handed a new role as Agnelli's replacement.
He said: "I am honoured and humbled to have been appointed by my fellow ECA Executive Board Members as chairman.
"The leadership, integrity and togetherness of our organisation has never been more required than at this pivotal moment in European football.
"I will provide my unconditional commitment to the entire football community: that means to all ECA Member Clubs from every European nation, and to the fans and communities they represent.
"I, alongside all my fellow ECA Board Members and Clubs, am looking to reinforce ECA in its role as the legitimate and singular voice of Europe’s clubs. Our game, adored by generations of supporters, will only prosper under unity, and it is our duty as the custodians of football to fulfil this obligation."
The ECA said: "Following the unprecedented events of recent days, which has seen attempts to undermine the entire European football community, ECA – representing the leading football clubs of Europe – welcomes the decision from its former member clubs not to pursue their purported 'Super League' project.
"ECA firmly believes this project could not succeed because football, at its core, is based on openness, sporting excellence and an inherent connection between everyone across the football family.
"Football is for everybody. Recent events have been a reminder that club owners are merely custodians of their clubs, which are historic beacons that mean so much to fans and their communities.
"ECA believes that it is the responsibility of every member club to ensure that we develop football and leave it in a better place for the next generation; not to dismantle it purely for financial gain."