Spurs were contemplating an evening of frustration as it looked like they would be held to a 0-0 draw in Portugal before things went very wrong at the death.
Paulinho nodded home from a corner and then with virtually the last kick Arthur Gomes sauntered into the box to convert and put Sporting top of Group D with two wins from two.
Conte told BT Sport: "It was a difficult result, when you lose the game you are not happy. I think that the game was unbalanced in the second half, we could score.
"We tried to win the game and then in the last 10 minutes we can do much better. They scored with a corner and we conceded the second goal after the 90 minutes.
"I think it is a pity. But a difficult game for sure, we tried to get a win but in the end we lost the game."
Spurs were far from their attacking best with Harry Kane, Son Heung-min and Richarlison starved of proper service in an uninspiring display.
They had some moments in the second half, which might have seen them go ahead, but instead of winning the game, Conte was left contemplating defeat.
However, the Italian switched his focus to Saturday's Premier League clash with Leicester.
"When you arrive you have to try and feed the box and have accuracy and go strong to attack the goal," he said.
"We had two or three situations where we can do much better. Now we have to try to rest and think of the next game in the Premier League."
One of Sporting's biggest threats was former Spurs academy player Marcus Edwards, who gave his old club the runaround and almost scored a wonder goal.
The 23-year-old, who former Spurs boss Mauricio Pochettino once compared to Lionel Messi, said the result was not made sweeter by the opposition.
"It doesn't feel extra special but it is a strange feeling playing against Spurs. I was there for so long," he told BT Sport. "But it was nice to see some players and staff.
"It is a proper family environment we have here so I couldn't be happier."