Conte labelled his players "selfish" after Tottenham drew 3-3 with Southampton, despite leading 3-1 with 15 minutes to go.
It came just two weeks after Tottenham, who are fourth in the Premier League, exited both the FA Cup and Champions League in the space of a week.
Conte is widely expected to be sacked, but Kulusevski, when asked if he was offended by the coach's comments, said: "No, because I know what I bring to the team every day.
"I know that I prepare myself to do as good as I can, and that's why I can always look myself in the mirror.
“Sometimes I know I don't play good enough, and I can take responsibility for that, but what he said is for him, that's his word.
“I respect him, and he helped me a lot during my career. So, he's still a very important man in our club and in my work.”
Spurs midfielder Pierre-Emile Hojbjerg suggested Conte needed to be "a little more precise" with his words, but Kulusevski believes the players can have few complaints after a poor run of form.
"He was very disappointed, as were us players, and we have to accept that," said the winger.
"We lost all the cups, we went out in Champions League also. So, I know that sometimes we have to be sad and angry, and that's how he took it.
"Somebody else will take another way; we just have to respect his words.”
As unlikely as it now seems, Kulusevski was then asked if he would still be happy to play under Conte and replied: "Yeah, absolutely.”
Reports this week revealed Allegri, who won five Scudetti in five seasons in Turin, had met with Bianconeri chief Agnelli.
That appeared to increase pressure on Pirlo, whose first season as a senior coach has badly gone off the rails.
Juve are fourth heading into Wednesday's game against Napoli, who are fifth on the same number of points.
After nine consecutive Serie A titles, Juve risk missing out on Champions League qualification for next season.
But Pirlo feels he still has the backing of Agnelli, who informed him of the encounter with Allegri, a coach who has been without a job since his departure in 2019.
"There is no position," Pirlo said ahead of the Napoli game. "I was warned by the president himself about the meeting with Allegri.
"Football is one thing, friendship is another. I have a daily relationship with Agnelli, we tell each other everything that happens.
"I knew about this meeting and I know I have his confidence, then obviously it's up to me to prove that I can be the coach for next season as well."
Pirlo might find the going tough against Napoli, as the Partenopei arrive in Turin on a four-match winning run in Serie A.
Napoli have also won their previous two games against Juve, while they have a joint-high five wins over the Bianconeri since the start of their sequence of nine championships in a row.
Pirlo will also be without Merih Demiral, Leonardo Bonucci and Federico Bernardeschi following positive coronavirus tests, but the coach insisted he had no issue with the game going ahead.
The fixture was originally scheduled to take place in October but did not go ahead as planned, after Napoli did not travel to Turin on the recommendation of their local health authority (ASL).
"We respect the protocol," Pirlo said. "We are in tune with what the ASL says. We will do what we have always done, we will present ourselves and play."
Paulo Dybala, left out against Torino on Saturday after breaching COVID-19 regulations, is back in contention, while Pirlo is keeping faith with Wojciech Szczesny and Dejan Kulusevski, who have each been guilty of recent on-field mistakes.
Juve had not committed a single error leading to a goal in Serie A this season until March but have since had three.
Szczesny's, against Torino, also saw Kulusevski - at fault against Lazio - give the ball away cheaply.
"Szczesny will play because after a negative performance there is always a desire for redemption," Pirlo said, adding: "I spoke to Kulusevski. I reassured him. Mistakes can happen - you have to raise your head."
Spurs were 3-0 victors over Sheffield United at Bramall Lane on Sunday, ending their Premier League season with a convincing win to finish fifth in the table.
Postecoglou voiced his frustrations after Tuesday's 2-0 defeat to Manchester City ended their hopes of Champions League football next term.
The Spurs head coach was far more relaxed after his side performed well in Sheffield, with Dejan Kulusevski twice on target, along with a goal for Pedro Porro against the relegated Blades.
Yet Postecoglou insisted his ambitions remain high as the Australian attempts to take Tottenham to the next level.
"Contrary to my general demeanour, I have loved every minute of it," former Celtic boss Postecoglou said of his first season in charge of Tottenham.
"It is a great challenge in the Premier League and taking over a big club that didn't have a great year last year. You understand it is not going to run smoothly, but I have enjoyed the whole season.
"I have got some lofty ambitions for the football club and until we reach that point I am not going to be smiling too much.
"As I said, all any manager wants is maximum effort and I have got that from everyone involved. I have enjoyed it and looking forward to pushing on from here."
Asked to summarise his first campaign in England's top league, Postecoglou continued: "It's been good, it's been eventful, it's had a bit of everything.
"I am obviously not delighted with the way we finished the season but in fairness to the players and staff we have been in the top five all season, in a year where there was a fair bit of upheaval.
"We finished eighth last year, player turnover, different football, different way of training, it is not easy to maintain a level when you are trying to do that.
"Even in our tough periods this year we have still been competitive for the most part."
Kulusevski scored his seventh and eighth Premier League goals of the season (36 outings), more than he managed in his first two league campaigns with Tottenham combined (seven across 48 games).
Only in the 2019-20 season with Parma has the Sweden winger scored more times in a league season (10 in Serie A), and Postecoglou hailed Kulusevski's returns.
He added: "I thought Deki was good. He's worked awfully hard this year without a lot of reward in the front third.
"We thought playing him through middle today would help us with his mobility and ability to run in behind. He did well.
"He always works hard but it's that sort of final third where we need him to get rewards and he got them today so he did well."
