It was the midfielder's first goal for the club and he later told BBC Sport he had grown frustrated by a lack of opportunities under Klopp. He became the Reds' youngest goalscorer in a Merseyside derby since an 18-year-old Robbie Fowler in 1994.
Unfortunately for Carlo Ancelotti's Toffees (still doesn't sound quite right), they simply could not find the back of the net, and Liverpool won the match through a stunning, curling effort from highly-rated academy prospect Curtis Jones in the 71st minute.
"But he showed his understanding of the game, his football skills are exceptional". You have to score, otherwise we ignore you? An unbelievable player, Scouser, very confident, can't wait to play in the first team.
It was Jones' first senior professional goal and one that quite clearly displayed his massive potential. And rightly so. He is in a very good way. I know we have to work. He's made big steps and will be a Liverpool player, if nothing unusual happens, 100 per cent. I'm not surprised he scored that kind of goal. He is for these situations.
Liverpool suffered an early blow through the injury of James Milner.
"All the rest of the night was absolutely ideal", Klopp said.
'I am not used to speaking to the players after the game but I am going to speak with them, ' said Ancelotti, whose side failed to lay a glove on Liverpool in a one-sided second half. "I loved each second of it". We are out of this competition.
Everton were profligate in the first half, and Calvert-Lewin - their form man - was particularly wasteful. We were a little bit unlucky and not precise.
"The defeat arrived because we were not able to keep a high intensity in the second (half)". We were not able to create opportunities. "We lost energy and confidence".