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."