Liverpool must beat Napoli 1-0 or by two clear goals on 11 December to reach the knockout phase and Klopp admitted: "We need Anfield again and we need to create an atmosphere which is pretty special".
It was a game littered with controversy, with Marco Verratti somehow escaping a red card for a reckless challenge on Joe Gomez.
But they were given a lifeline on the stroke of half-time when Mane robbed Marquinhos, who up to that point had been commanding, and was brought down just inside the penalty area by a lunging Di Maria.
"When the game starts like that it's hard to gain confidence", Klopp told BT Sport.
A number of the home team's players received treatment during the game and Liverpool's players often berated the officials as they believed they were time-wasting.
"A little hurdle was the 500,000 interruptions in the second half and the referee still thinks he did everything right". Tonight, we look like butchers. We were not that good that night but they played really well. But that's to deal with, that's the job for us to deal with, and if the ref lets it happen then you have to deal with it as a team.
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Last week it was reported that Neymar and Kylian Mbappe both could miss the Champions League clash vs Liverpool due to injuries. "He is not the nicest boy on the planet now", said Klopp of the England worldwide defender. "The penalty - I have no idea why it was a late decision". It was inside [the box] but that doesn't mean it was a foul. The home midfielder Marco Verratti was one of those booked for a awful foul on Joe Gomez that could easily have resulted in a dismissal. Still, we were in the game. It's a tight game in a very important competition. You can give yellow cards for everything. Five, six, seven or so?
Other star guests amid an ecclectic mix at the game included veteran rocker Mick Jagger - who was sitting one row behind Khabib - and Hollywood star Leonardo DiCaprio.
Klopp expanded on his criticism of PSG's antics in a further post-match television interview.
The win lifts Spurs level on points with Inter (ahead via tiebreaker), but they have to go to an already-qualified Barcelona in the group finale, while Inter is at home against last-place PSV.
"Unfortunately, negative aggression doesn't help in football".