The two sides had played out a 0-0 draw at the Deutsche Bank Park last week, but Frankfurt had the ball in the back of the net with just 14 minutes gone on Wednesday as Daichi Kamada slotted home following a mistake from Eric Dier.
A brace from Son Heung-min alongside Harry Kane's penalty turned the tide in Tottenham's favour before half time, and the Lilywhites would seemingly see out a straightforward win after Tuta was sent off for two bookable offences just before the hour mark.
However, substitute Faride Alidou headed home from a corner in the 87th minute to set up a nerve-wracking finale, and Kane missed the chance to restore Tottenham's two-goal lead as he blazed a late penalty over the bar.
Tottenham ultimately survived that late scare to move top of Champions League Group D, but Conte admitted that his side were on the cusp of a "disaster" in the dying embers.
"It is difficult to start from the end of this game because we played a really good game, despite conceding a goal, that we could be much better in this situation, but our reaction was an important reaction and we created many chances to score. We scored three times and [Kevin] Trapp was their best player in the whole game," football.london quotes Conte as saying in his post-game press conference.
"That is the positive aspect from the game. The negative aspect is the final part and it has to be a big lesson for everybody, for me, for the players. The game finishes when the referee whistles three times. In the last part of the game, everybody conceded the game ended and for this reason we made a big mistake.
"When we missed the penalty honestly, I was a bit scared, because I thought everything can happen. We are talking about a really good performance but the final part we have to take a big lesson, everybody. Myself and the players, everybody conceded the game ended. Maybe also the stadium and the fans.
"For sure the lesson has to be that no one has to concede the game and also if you are leading 3-1, you are playing against 10 men and everything seems on the right path, but football is difficult.
"It is difficult, now we are talking with a smile because we won. But imagine if this game finished a draw. That would have been a disaster."
A calamitous night for Frankfurt defender Kristijan Jakic saw the Croatian bundle over Kane for Tottenham's first-half penalty, and his dreadful attempt at a backheel pass saw the ball break kindly for substitute Bryan Gil late on.
The Spaniard's dancing feet saw him win a second spot kick for Tottenham as Hrvoje Smolcic stuck out a leg, but Kane could not repeat his previous success from 12 yards as he sent his penalty flying over the bar, much to the shock of Tottenham fans.
However, Conte has no concerns over the 29-year-old's "killer" ability from the penalty spot and believes that his wayward effort was simply down to fatigue, adding: "You know we are talking about a player that is very difficult to miss penalties.
"He's a killer and I think that also today in the end he was really really tired because he ran a lot. He played for the team and I think he played in a fantastic way today."
Marseille's 2-0 win over Sporting Lisbon has seen Tottenham open up a one-point lead over both sides at the top of Group D, and the Lilywhites will qualify for the knockout stages if they beat the Portuguese giants on October 26.
Conte now prepares to resume Premier League duties with the visit of Everton to the Tottenham Hotspur Stadium on Saturday evening, and the Spurs boss confirmed that Dejan Kulusevski - who missed Wednesday's game despite partially returning to training - is likely to be available for that encounter.