It was Parker's first game in charge following the sacking of Claudio Ranieri, a former Chelsea boss, after less than four months in charge.
"We knew how much this fixture means to the fans", said Pickford.
"We focus on our next game, everyone wants to be top of the league and we can not change the situation at the moment", the Liverpool defender added.
"The only way that you can win something is to stay calm but lively, critical but confident, and in the end believe in your chance", said Klopp.
The good news for Everton is that they have no real injury concerns ahead of the game, with veteran Leighton Baines being the only player who is definitely ruled out due to a back problem. I watched Match of the Day last night and saw the celebrations of Man City, they had 900 chances and scored one goal [in a 1-0 win at Bournemouth], a shot with the wrong foot.
These are the days that can define the title race, and Liverpool lacked a leader, an inspiration to overcome a resolute, well-organised Everton side.
Marco Silva's side snapped a three-loss streak to beat Cardiff City 2-0 in the Welsh capital on Tuesday, a victory that pushed them above West Ham into ninth place.
Marco Silva has responded to Jurgen Klopp's claim that the Merseyside derby is "a kind of World Cup final" for Everton by pointing out how Liverpool celebrated their late victor in the last one.
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City, who won 1-0 at Bournemouth on Saturday, have 71 points while Liverpool are on 70 with both teams having nine games to play. "It shows how well we are doing that they want to stop us". "We don't lose our nerve", he said.
Van Dijk insists that the Reds deserved to win at Goodison Park and it was telling how the home crowd reacted after the final whistle.
"You look and you think 'could they have been more proactive with the substitutions that they made?'".
Liverpool were poor, with Mohamed Salah missing a number of opportunities at Goodison Park.
"The wind does not help and there was a lot today. I think it was a fair result, not too many chances were created by either team".
"Not flawless but good enough - getting a point from Everton is always a success because it is our most hard away game of the season".