The former Juventus and Chelsea coach vented his anger from the technical area several times during the first half as his lacklustre team were out-battled by injury-hit Leeds.
Boos rang out at halftime with Leeds ahead through Daniel James's close-range effort but Conte earned his money at the break, galvanising his players for a vastly-improved second half in which goals by Pierre-Emile Hojbjerg and Sergio Reguilon earned Tottenham the points to move them up to seventh.
Conte celebrated each goal like a man possessed, spent the closing stages conducting the fans and could hardly contain himself as the final whistle sounded at the end of his first Premier League home game in charge of the club.
"In the first half, we struggled. Physically, tactically and in our intensity, we struggled," Conte said.
"I think in the second half we changed things and we wanted to play with the same intensity as Leeds.
"We won the game, we deserved to win. We played attractive football and the crowd was with us."
The match statistics showed that Tottenham were outrun by Marcelo Bielsa's tenacious Leeds in the first half.
But that was reversed in the second half as Spurs showed the intensity Conte has demanded throughout his managerial career.
"At halftime, the players showed me they could win this game," Conte, who resisted the urge to make any substitutions at the interval, said.
"In the second half, I corrected the situation. I look at the stats and Leeds are the best in the league for running. In the second half, we beat them in intensity.
"I'm pleased with the players, they showed good personality and in the second half put pressure on Leeds in every part of the pitch. To win this way is good."
Reguilon, who scored his first Premier League goal to snatch the points, epitomised Tottenham's second-half display with an energetic shift up and down the left flank.
"We put in an amazing effort. We are so happy and so, so tired," the Spaniard said. The players, we know we needed to give more in the second half."
Leeds were missing the likes of Raphinha, Rodrigo and Patrick Bamford and after deservedly leading they appeared to run out of steam in the second half.
They are in 17th place, just two points above the relegation zone and need to start picking up points.
"In the first half we played better, in the second half they did," Bielsa said. "The difference in the second half was bigger for them than we managed to achieve in the first half.
"I think the result was fair."
England midfielder Kalvin Phillips, who played in central defence in the first half, said it was not a time to panic.
"The way we play football we'll eventually stack some more points on the board," he said.