The fiery Italian admitted he was 'very upset' as he spoke to the media in his post-match press conference, went on a rant about the lack of 'honesty' in football, and then left after answering just one question.
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Harry Kane scored in stoppage-time to seemingly complete a comeback to beat Sporting Lisbon 2-1, after going in at half-time 1-0 down.
The striker fired home in the fifth minute of added-time to spark wild celebrations on the pitch and in the dugout, with Conte dancing down the touchline with the hosts believing the effort had sent them through to the last-16.
However, their celebrations were halted by a VAR check and, after a four-minute wait, it was ruled that Kane was ahead of the ball when Emerson Royal's header hit Flavio Nazinho and ricocheted into the path of the striker to put the ball in the net.
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Conte was sent off for his angry protestations, while Sporting players and staff were then left celebrating the decision, which meant ex-Spurs ace Marcus Edwards' first-half strike against his former club - which was later cancelled out by Rodrigo Bentancur's 81st-minute header - left all four teams in Group D with a chance of making the knockout stage going into the last game.
And it's fair to say Conte was not happy, as he answered just one question with a two-minute rant about the 'unfair decision' before rising from his chair and stalking out of the press room.
"I think there are moments that maybe you can be a bit intelligent to understand you have just disallowed a regular goal because the goal was regular, the ball is in front of Kane," Conte began - which, unsurprisingly, is just what a fuming Jamie O'Hara said on talkSPORT after the full-time whistle.
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"And then the VAR. I repeat you know I don't comment on referee decisions but the VAR, this season, I don't know why between Premier League and Champions League, we are not so lucky.
"I don't know why until now we are also the only team who repeated the penalty and every penalty I go to see, if the keeper move on line, I see a lot of the time. I want to see repetition of a penalty in Premier League.
"I think we are not so lucky with VAR but I think they create big damage. I would like to see if this type of decision you can take with a top team, in an important game, yeah I would like to see if the VAR is so brave to take this decision.
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"I repeat this is an unfair decision because the ball is in front of Kane. Sorry, but I am really upset because sometimes you can accept this situation and sometimes I think it is not good because I don't see honesty in this type of situation and when I don't see this I become really, really upset."
The result means Tottenham need a point at Marseille on Tuesday to qualify for the last-16 and Conte called on the club to speak to the relevant people over the VAR decision.
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He added: "For the game we played the first-half with low intensity and Sporting Lisbon deserve to stay 1-0 up and at the end of the game after our second-half I think we deserved to get three points.
"But now for this decision we have to wait to the last game against Marseille and I repeat this decision, yeah it creates big damage.
"I hope the club understands this and then in the right situation they also speak with the people they have to speak to, because otherwise it is only the manager to speak.
"I think the club has to be strong because I repeat this situation creates big, big damage. Now we don't know what will happen next week.
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"If we go out, then I want to see.
"OK, thank you very much," Conte said finally as he quickly left.