Klopp claimed the Barclays award for the second time after guiding his side to victory in all of their seven Premier League matches, with a league-high 22 goals scored and only three conceded.
"It’s nice, the icing on the cake," said Klopp, whose first award came in September 2016. "It was a very successful but difficult month.
"Each game felt like the most important one of the season. It was unbelievable. The intensity was massive but that's what made it a special month."
As to the basis of Liverpool's perfect record in December, Klopp pointed to the support from his staff.
"One hundred per cent teamwork," he said. "I know a few things about football but my best skill is to bring really good people together.
"I lead that group, that's true, and I have to make final decisions but I can only make good decisions if the information I get is brilliant.
"With the group I have here, if you can mix up the potential of the group with the best attitude you can get, you get quality. That's what we did in December."
"It was a fantastic month for us," he said. "Some great games and I have enjoyed every bit of it."