Carlo Ancelotti's side should have led early on but Dominic Calvert-Lewin, Mason Holgate and Richarlison all shot too close to Adrian, who reacted instinctively on each occasion, while stand-in Liverpool captain James Milner was injured in attempting to prevent the first opening.
Everton created a few very good chances in the first half. I told the boys they I have to be proud of them as they were exceptional'. You have to score, otherwise we ignore you?
'The line-up of Liverpool didn't effect our idea of how to play. "It was to play a good game".
The Toffees looked for the equaliser to take the match into a replay, but their Merseyside neighbours opted otherwise and progressed to the fourth round instead.
"The second half was different".
"We had a lack of energy and it was there that we lost the game".
After a performance which former Liverpool defender Jamie Carragher described as the worst derby display at Anfield in 35 years, the situation Ancelotti has inherited was laid bare to him and it is something he hopes to address in the transfer window. "Everyone is behind him, he is behind the team so we are together, we are like a rock at the moment and it's hard to break a rock".
Liverpool manager Jurgen Klopp was understandably delighted after his calculated gamble of giving the majority of his first-team stars the day off paid dividends.
"He's the best right now because he got a lot of stuff here", Adrian 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.