Conte's tenure at Spurs looks set to end after Saturday's explosive rant at Southampton saw him accuse his own players of being "selfish", while he made repeated references to the culture of a club that has "never won something" during a passionate 10-minute monologue.
While Conte later clarified to the board that his comments were aimed at his underperforming squad, he is still expected to leave before Tottenham's next match away to Everton on April 3.
Swedish forward Kulusevski followed team-mate Pierre-Emile Hojbjerg in discussing the recent press conference during his time away with his national team.
Asked if he would be happy to keep working with Conte, Kulusevski told Sky Sports: "Yeah, absolutely.
"He was very disappointed, as (were) us players. We have to accept that. We lost all the cups, we went out in Champions League also so I know sometimes we have to be sad and angry.
"That is how he took it. Somebody else would take it in another way but we have to respect his words."
Conte's frustration boiled over after Tottenham let a 3-1 lead slip to draw at bottom-of-the-table Southampton and miss out on the chance to head into the international break in third position in the Premier League.
Spurs had exited both the FA Cup and Champions League earlier in the month to increase the pressure on Conte, who had been expected to leave in the summer when his current terms expire.
That departure is now primed to be accelerated and first-team coach Ryan Mason could be given the reins for the final 10 fixtures of the season, the PA news agency understands.
Mason, who performed a similar job towards the end of the 2020-21 campaign, has been present at Hotspur Way this week to work with Barcelona loanee Clement Lenglet, Japhet Tanganga, Arnaut Danjuma and Lucas Moura, as well as back-up goalkeepers Brandon Austin and Alfie Whiteman.
Conte flew back to Italy after the 3-3 draw at St Mary's, a trip which was already planned and has been the case during international breaks throughout his time at the club.
When the 53-year-old returns to London remains to be seen but Kulusevski insist he has taken no offence to the comments of his experienced manager.
"No, because I know what I bring to the team," Kulusevski added.
"Every day I know I prepare myself to do as good as I can and that is why I can always look myself in the mirror.
"Sometimes I don't play good enough and I can take responsibility for that but what he said, is for him.
"It is his words but I respect him and he help me a lot during my career. He is still a very important man in our club and in my world."