Victory would have ensured passage into the knockout rounds of Europe's premier club competition for Spurs but instead they will have to wait until the last matchday against Olympique Marseille to be sure of progress.
Former Spurs youngster Marcus Edwards gave Sporting a first half lead and the home side had to wait until nine minutes to the end before Rodrigo Bentancur found an equaliser.
Harry Kane appeared to have struck a winner in stoppage time but his celebrations were cut short after VAR intervened and Conte was sent off by referee Danny Makkelie for taking his protests a little bit too far.
"About the end, I think that the ball was in front of Kane and the goal is a goal. I don't understand the VAR, the line that they put," Conte told BT Sport.
"It's very difficult to comment on this decision and VAR, I think, is creating a lot of damage.
"I want to see if, in another stadium or with another big team, they are ready to disallow this type of goal. I'd like to know this.
"[I see] a lot of injustice. I don't like this type of situation. I see no positive things."
"All the people came inside the pitch after the decision to disallow the goal," Conte added. "He came to give me a red card, maybe because I was the most popular person going onto the pitch."
