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.
Football in Italy is due to return this month after being suspended since March following the outbreak of COVID-19.
Juventus were a point ahead of Lazio when the campaign was stopped as they pursued a ninth Scudetto in a row, with Inter a further eight points back with a game in hand.
A serious second wave of infections would likely see Serie A brought to a standstill again and Bonucci thinks it would be better for all concerned in that instance if 2019-20 was simply scrapped.
"I hope we get to the normal end of the championship," the Juve defender told La Gazzetta dello Sport. "If that didn't happen, a lot of stories, controversies, appeals would come out.
"I'm not in favour of other hypotheses. If it stops, it's better to finish things there and not assign anything.
"Hopefully, we'll get to August 2 and declare a winner. Hopefully, it's Juve."
Juve will resume the season with the second leg of their Coppa Italia semi-final against Milan on June 12, with the aggregate score 1-1.
The Bianconeri are pursuing a possible treble in Maurizio Sarri's first season in charge since he took over from Massimiliano Allegri.
Comparing the two coaches, Bonucci admits to being "pleasantly surprised" by Sarri's way of working.
When asked to name the differences between Allegri and Sarri, he said: "They're obvious. Allegri is really good at managing the dressing room, the most difficult moments of the season, to make the team understand how to manage the tempo of a match. In his five years, he was a master at this.
"Sarri is meticulous, passionate about tactics, someone who likes to make the team play well. He's also learned in these months with Juve what it means to be Bianconero.
"I've seen us grow significantly. He has a wealth of football knowledge, but he has been able to question himself. He had the humility to understand the dynamics of the collective. I was pleasantly surprised, really."
Liverpool goalkeeper Alisson and full-back Trent Alexander-Arnold are also included, although there is no place for Mohamed Salah.
PSG's attacking trio of Lionel Messi, Neymar and Kylian Mbappe are among the forwards, as is Manchester United star Cristiano Ronaldo.
Veteran Dani Alves also won enough votes to make the list, even though the 38-year-old, who recently rejoined Barcelona, only played 16 times in domestic competition in Brazil this year.
Professional footballers across the world were asked to vote for the three players they considered to have the best seasons during the 2020-21 season among goalkeepers, defenders, midfielders and forwards.
FIFPRO said: "For the first time in 17 years, FIFPRO is updating the announcement about the most-voted players, reducing the shortlist from 55 to 23. This has been done to resemble a real-life 'squad' which, usually for international competitions, is the number of players involved.
"The three goalkeepers, six defenders, six midfielders and six forwards with the most votes earned a place in the 23-men World 11 'squad'. To complete this elite selection, the two remaining outfield players with the most votes were added."
The keeper, three defenders, three midfielders and three forwards with the most votes will be chosen for the World 11, with the remaining spot assigned to the outfield player with the next highest number of votes.
The final 11 will be announced at The Best FIFA Football Awards ceremony on January 17.
FIFA FIFPRO MEN'S WORLD 11 23-PLAYER SHORTLIST:
Goalkeepers:
Alisson (Liverpool, Brazil)
Gianluigi Donnarumma (Milan/Paris Saint-Germain, Italy)
Edouard Mendy (Chelsea, Senegal)
Defenders:
David Alaba (Bayern Munich/Real Madrid, Austria)
Jordi Alba (Barcelona, Spain)
Trent Alexander-Arnold (Liverpool, England)
Dani Alves (Sao Paulo/Barcelona, Brazil)
Leonardo Bonucci (Juventus, Italy)
Ruben Dias (Manchester City, Portugal)
Midfielders:
Sergio Busquets (Barcelona, Spain)
Kevin De Bruyne (Manchester City, Belgium)
Bruno Fernandes (Manchester United, Portugal)
Frenkie de Jong (Barcelona, The Netherlands)
Jorginho (Chelsea, Italy)
N'Golo Kante (Chelsea, France)
Forwards:
Karim Benzema (Real Madrid, France)
Cristiano Ronaldo (Juventus/Manchester United, Portugal)
Erling Haaland (Borussia Dortmund, Norway)
Robert Lewandowski (Bayern Munich, Poland)
Romelu Lukaku (Inter/Chelsea, Belgium)
Kylian Mbappe (Paris Saint-Germain, France)
Lionel Messi (Barcelona/Paris Saint-Germain, Argentina)
Neymar (Paris Saint-Germain, Brazil)
Italy won their first European Championship since 1968 by defeating England on penalties last July at Wembley.
Roberto Mancini's side return to Wembley to meet Argentina in the 'Finalissima' between the Euro 2020 winners and Copa America champions.
Italy have struggled since their last visit to England's national stadium; missing out on a second straight World Cup after falling to a stunning play-off defeat against North Macedonia.
Bonucci has replaced Giorgio Chiellini as skipper of both Juventus and Italy, with his defensive partner heading for the exit door in Turin and announcing he will retire from international football following the game against Argentina.
The 35-year-old Bonucci is relishing the challenge of facing Lionel Scaloni's side.
"They are among the best in the world, Argentina hasn't lost in 31 games and it's no coincidence," he told reporters on Tuesday.
"We need maximum commitment and respect. We must start again and lay the foundations to bring Italy back to the top."
Argentina captain Lionel Messi suggested Italy would have been favourites for the World Cup should they have appeared in Qatar, and Bonucci expressed his gratitude for those comments.
"The fault is ours, it took very little to be able to play in something truly unique for a player's career," he added.
"We thank Messi for the kind words he said about us; tomorrow two winning national teams will meet and we want to put on a show to take the trophy home."
Bonucci hailed Messi, who will aim to guide Argentina to their third World Cup win and first since 1986.
"For a player who has won so many Golden Balls it is difficult to find words to described him," the Juve defender continued.
"He was, and still is today, with Cristiano Ronaldo as one of the best in the world – great respect will be needed."
As for Chiellini's international retirement, Bonucci hopes to give him a fitting send-off as he outlined his own plans for captaincy.
"We must enjoy this last day with him, he was a great companion on the pitch and in life," he said. "From the day after tomorrow I will continue to do what I have always done, to be an example.
"From Chiellini I learned the ability to work out difficult situations in a short time and find the solution.
"That is the secret that made Giorgio a great person and a great captain, I'll try to smooth out the flaws. My team-mates will have to help me too, just as we helped Chiellini and [Gianluigi] Buffon."
The outbreak of the virus, officially named COVID-19 which originated in China, forced four Serie A matches to be postponed on Sunday, including the clash between Inter and Sampdoria.
The move came as part of preventative measures taken in Italy after two people died in the country.
Italian prime minister Giuseppe Conte has said all this week's top-flight fixtures could yet be cancelled too, while reports suggest Juve will host title rivals Inter behind closed doors in Turin on Sunday.
Sarri, though, has refuted suggestions his club's fans should have stayed at home instead of travelling to France for the first leg of their last-16 tie.
"It's a European and global problem, not an Italian one," he told a media conference. "In Italy, we made 3,500 tests for coronavirus and therefore had many more positive tests.
"In France you had about 300 tests and so obviously the average who are positive is much lower. If you did as many tests as we did, you'd probably have as many positives too. Therefore, our fans have every right to be here."
Juve have not won European club football's biggest prize since 1996, but Sarri does not believe his future is dependent on ending that drought this season.
"I don't know what my future depends on, but the president pointed out that this is a three-year project," he added. "I have great faith in what my president says, as he tends to be pretty clear.
"It's very difficult for any Italian club to chase this dream because we were the leaders 20 years ago, but we have been overtaken due to various reasons in the last couple of decades.
"A dream is not to be underestimated. If you chase a dream and achieve it, that is ecstasy, whereas if you don't achieve it, it was still a wonderful journey."
Giorgio Chiellini could make his first European appearance of the season after a serious knee injury ruled him out for five months.
The centre-back has featured in Juve's last two Serie A games and has subsequently been named in the squad for the trip to France, much to the delight of his defensive partner Leonardo Bonucci.
"We both like to not only play football, but also talk during the game, communicate with our team-mates and help the younger players to make the right movements," Bonucci said. "If there are two of us doing that, it's easier.
"There is also a language issue, because with Matthijs de Ligt we are trying to communicate in English while he learns Italian. It's not quite the same, but we're getting there and improving our communication. With Giorgio there, we can speed the process up."
