The Reds after opening the score through Fikayo Tomori's own goal received two goals in a matter of minutes to throw away the lead before half-time.
But Liverpool not willing to lose their first Champions League game produced another amazing comeback in the second-half.
The Merseyside club's comeback was complete with goals from Mohamed Salah who missed a penalty in the first-half and Jordan Henderson.
Revealing what motivated the unforgettable moment at Anfield, Klopp disclosed he refused to demonstrate angry antics at his players during the half-time team talk.
"I wasn't angry [at half time]," Klopp said after the triumph.
"We saw it coming and tried to get the message across but it didn't work out because of the outstanding atmosphere in the stadium.
"We started complicating it. We showed the boys some things at half-time and we organised things."
AC Milan, making a first Champions League appearance since 2014 could have registered a first win but were denied by the the 2018-19 Champions League winners.
Liverpool are poised in winning the Premier League title this season and are yet to taste a first defeat after four games.
Liverpool will be hoping to extend their winning streak when they host Patrick Viera's Crystal Palace who will be visiting Anfield on the back of a first victory over Spurs.
