Aurier thought he had given Spurs a 2-0 lead after 67 minutes but the VAR ruled Heung-min Son a fraction offside in the build-up – a decision that looked harsh on the visitors.
Leicester equalised two minutes later through full-back Ricardo and James Maddison's 83rd-minute strike completed the turnaround to leave Spurs still without an away win since January.
Pochettino was previously one of the most outspoken critics of VAR but he refused to blame the technology for the defeat, while admitting the decision changed the mood at the King Power Stadium.
"You get the benefit or not get the benefit, it's fair or not fair, offside or not offside – I'm not going to talk [about VAR]," Pochettino said afterwards. "I'm only going to say that we all accept the system in the game and now I am not going to complain. I trust in the referees and if the referees say it was or wasn't I'm not going to complain.
"I think we need to analyse the game in a different way and not include the VAR. We need to accept that it's completely fair, the rules. I'm not disappointed with that, I'm disappointed because we conceded two goals and the emotion of the game changed. Giving that decision to Leicester made that thing happen in the last 10 minutes.
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"I am not blaming VAR, please take me in the way [I mean]," he added. "At 2-0, the game is going to be different, when VAR disallowed the goal: 2-0 is not the same as 1-0 with 80 minutes. That is normal that it changes the emotions. For us it was a massive disappointment and for them it was a massive belief for all the people and fans to keep pushing and they found the way to score a goal. In the end, we all thought it was going to be a draw and the goal appeared from long distance and it killed our feeling."
Spurs have now picked up eight points from their opening six league games and thrown away leads in three consecutive away matches, following from the 2-2 draws at Arsenal and Olympiacos.
The manager claimed "everything is against" his side but praised their display for 83 minutes, which came after they returned from Athens at 4am on Thursday morning.
"The performance I think was good," he said. "After Wednesday, a long flight, not too much time to recover I think the performances was fantastic. I think we were the best team on the pitch for 83 minutes, of course but now that changed completely in the last seven or 10 minutes the feeling.
"The feeling before was that we dominated and with a different result we are talking in a different way, but we need to be fair in the way we are going to assess this. The team behaved very well with a great attitude and played in some moments very good football. I am happy with the performance, disappointed with the result. In this type of period where everything is against us, that is the moment to be tough and work hard and be positive."