The Reds won both the English League Cup and FA Cup, beating Chelsea in penalty shoot-outs at Wembley on both occasions.
But Liverpool lost out on the Premier League title to Manchester City by just a point after both Klopp's men and Pep Guardiola's side won their respective matches on Sunday's final day of a thrilling campaign.
Klopp, collecting his accolade at the LMA Awards dinner in London on Tuesday, said: "It is a great honour and it was an insane season.
"The last matchday when only two games were meaningless and in the rest, we all played for absolutely everything.
"It was not the best outcome for us, but we are already over it."
The German, paying tribute to his backroom team, added: "When you win a prize like this you are either a genius or you have the best coaching staff in the world -- and I am here with all of my coaching staff, they know how much I appreciate them."
Klopp also collected the Sir Alex Ferguson Trophy, named in honour of the celebrated former Manchester United boss, which is voted for by the full membership of managers across all the divisions in English senior football.
"This being voted for by my colleagues is obviously the most important prize you can get," Klopp said.
"I don't believe in individual prizes in football generally, it is a team sport and I would be nothing without these boys there.
"It is all about what we can do together and what we did together."
Liverpool may have been denied an unprecedented quadruple by City, but they will now try to add the Champions League to their impressive trophy haul this season when they face Real Madrid in a Paris final on Saturday.