Spurs claimed a point at Anfield in May after a battling display in a 1-1 draw which proved crucial in the race for the title after Manchester City beat the Reds to first spot by a single point.
Klopp did not hold back after the stalemate and insisted he could not coach the type of football that was played by Tottenham, who had only 35 per cent possession on the night but did also have the same number (three) of shots on target as the hosts.
But Conte admitted ahead of Sunday's fixture: "Yeah, but if you remember he lost the Premier League for this result, so I understood his frustration.
"They lost the Premier League because of that result. They lost the Premier League for these two points and you know instead we reached the Champions League with that draw. It's OK, every coach has to speak for his team.
"For every coach it's important to understand the best strategy to reach a good result. Honestly, I have seen again the last game we played against Liverpool and, if there was a team that deserved to win it was Tottenham, not Liverpool.
"But I understand after the game when you felt you lost the Premier League to say something wrong against another team, but he said sorry because he understood. No problem for me. When you are angry it's very difficult sometimes to control your emotion."
When Klopp and Conte do battle this time, the title will be far from the mind of the German after a difficult first half of the current campaign.
The Reds have been wildly inconsistent with points dropped against Brighton, Nottingham Forest and Leeds in recent league fixtures, despite also claiming excellent victories over Man City and Napoli.
Conte stuck up for Klopp in Friday's press conference and conceded that, without the challenge of Liverpool, Pep Guardiola's City could have dominated the Premier League like Juventus did in Serie A when they won nine consecutive league titles between 2012 and 2020, a run started by the Spurs manager.
He added: "Without Liverpool, I think maybe Manchester City could do in the same way like Juventus was in Italy, so for this reason they have to be proud to reach this level.
"I think they improved a lot in these years during the transfer market with the big, big signings and this is a positive thing I'm telling to Liverpool because you can have money to spend, but if you waste your money, you don't sign good players, you can have whatever money you want, but you have to spend it in the best possible way.
"I think that Liverpool did this in this period, otherwise I think it was really, really difficult to become the first rival for Manchester City. For this reason, they signed really, really important players. They spent money, but, I repeat, I'm talking in a positive way because for sure Klopp has changed Liverpool.
"The club gave him the possibility to invest because at the end you can work what you want, to work a lot, to work and not to sleep during the day, but at the end you know you need important players, you need really strong players if you want to win, if you want to go to another level."
Conte was quizzed again about Spurs' plans for January but struck a cautious note of warning while insisting he was unsure if they would spend big.
"Honestly, I don't know this," he said.
"For sure, the life will always be more difficult in the future. For sure, Tottenham has to have the challenge with a team like Newcastle, also Arsenal.
"Arsenal in the last three or four years, every season they invest money and now we are talking about a really, really good team with a really good coach, but in England it will be really, really difficult in the future.
"I think in every situation the most important thing is to be honest. To be honest with the fans, to be honest with the ambition, not to tell lies or to promise and this is the right way for every club.
"Because to tell good lies is not good. It's better to be honest, to tell the truth also if it's a bad truth, to (still) be honest. Honesty will pay always, always."