Mohamed Salah's second-minute penalty and a late Divock Origi goal settled what was not a classic at the Metropolitano Stadium, as Liverpool made up for their defeat in last year's final against Real Madrid and the deflation of missing out on the Premier League title to Manchester City.
"We were all pretty much crying on the pitch, because it was so emotional, it was so big, it means so much to us," Klopp said.
The revered German has his first trophy as Liverpool manager, three and a half years on from his arrival at the club. This result saw him end a run of six straight defeats in finals.
For Salah there was redemption after injury ruined his night against Real a year ago, and for Liverpool it is now half a dozen European Cups, as they further cement their status as one of football's most storied clubs.
They now have more than Barcelona or Bayern Munich, and twice as many as their greatest rivals, Manchester United. The biggest party is still to come. "Tomorrow, going to Liverpool and having something to celebrate, that is big, and I am really looking forward to that," said Klopp.
"When we drive through the city then we will all realise what these boys have done."
Perhaps the occasion was just too much for Tottenham in their first ever appearance in the Champions League final. They have now lost all three meetings with these opponents this season, winning just one of their last 15 encounters.
Mauricio Pochettino's decision to start Harry Kane after nearly two months out did not pay off, and he is still looking for his first trophy after five years in charge. Kane fails to make impact Nevertheless, if they can keep him, and with the impetus from the move to their new stadium, maybe they will be back on such a stage before long.
"It is so painful but at the same time we need to be calm and feel proud. The season was fantastic," he said.
That Spurs were here at all was remarkable, Lucas Moura's sensational hat-trick that dumped out Ajax in the semi-finals capping a memorable Champions League season all round.
The stage was set for this match, only the second all-English final, but after all the hype and the stories of fans paying thousands for tickets for a game they simply could not miss, this was a strangely subdued affair between the two goals.
Perhaps the stakes were simply too high, or perhaps the three-week break since the end of the Premier League season was to blame.
Most likely the suffocating Madrid heat -- Klopp's description of "pretty warm" was an understatement -- impacted on the players and prevented this from being like a typical Premier League clash.
However, it might also have been a result of the opening goal coming so early, badly affecting Tottenham's confidence. Pochettino had opted to start Kane after an ankle injury, meaning Lucas was on the bench. Kane hardly touched the ball. Eight members of Liverpool's team also started last season's final, when Salah went off injured and in tears in the first half.
This time Liverpool were the ones celebrating early on, Slovenian referee Damir Skomina pointing to the spot inside 25 seconds when Moussa Sissoko blocked Sadio Mane's cross with his arm. Salah confidently blasted home the penalty for the second-fastest goal ever in the final of the modern Champions League. The only faster effort was Paolo Maldini's goal for AC Milan against Liverpool in Istanbul in 2005, when the Anfield side famously won on penalties.
Spurs just did not get going, and there was none of the frenzied pressing and attacking associated with Klopp's side, although Trent Alexander-Arnold and Andy Robertson both came close in the first half.
Tottenham improved after the break, but Virgil van Dijk was immense for Liverpool and there was no way past Alisson, the Brazilian saving well from Son Heung-min and Christian Eriksen late on.
It was left to Origi, one of the heroes of the stunning semi-final win over Barcelona, to wrap it up with three minutes left as he swept home inside the box.