Spurs were staring down the barrel of a Boxing Day defeat at the Brentford Community Stadium with goals from Vitaly Janelt and Ivan Toney putting them 2-0 down.
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But goals from Harry Kane and Pierre-Emile Hojbjerg in the second half saw Conte's men salvage a draw that had appeared unlikely.
Spurs have now gained 14 points from losing positions in the Premier League this season, more than any other club in the division.
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And while Conte is proud of the resolve his players he lamented their slow starts to matches with Spurs now falling behind in their last NINE outings.
"In one side I have to be happy because of the way we played in the second half, the energy, desire and intensity and when you play like this you create problems," Conte told the media. "On the other side this is now nine games in a row we concede the first goal.
"It's important to be stable for a team that wants to try to stay in a good position in the table. To concede for many goals the first goal or two goals, we have to make good reflections. We have to find solutions.
"For me this is the first time in my career to concede first nine games in a row. They showed great character but we have to start in this way… a difficult team and they drew against Chelsea and beat Manchester City.
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"It's not easy to press them because they can hit it long and Toney is very good. I want to underline how good they are but we could have won."
Spurs' defensive struggles led to questions about whether they would be looking to strengthen in that position during the January transfer window but Conte suggested he's satisfied with what he's got.
"Now we have recovered also Japhet Tanganga, also the first game of the season," Conte added.
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"He started a lot with his knee. He needs a bit of time to get into the game. I'm pleased for him to play a game today.
"With central defenders we are good, we have to continue to work. Cuti [Cristian] Romero comes back to training tomorrow. In one side, I'm a bit disappointed in the other we're scoring a lot of goals and creating a lot."