Everton are facing possible relegation for the first time in 71 years but manager Frank Lampard said he remains "very committed" to the job.
Everton are in the relegation zone, in 18th place and two points behind 17th-placed Burnley, who have played one more game.
Lampard's team have six matches remaining this season and host Chelsea on Sunday.
"I am very committed," Lampard said. "I really don't want to get into the headlines or ins and outs of that, but absolutely [I am committed]."
The former England international was unwilling to discuss the consequences if Everton got relegated but promised to stay at the club as long as needed.
"Sometimes people from the outside ask me, because of the position we are in: 'Are you enjoying it, with all the pressures of it?' I absolutely love it," Lampard said. "I have been welcomed incredibly well by the fans and supported by them and I will do everything to get this club back to where I want it to be."
Meanwhile, Chelsea manager Thomas Tuchel said Lampard will always be a Chelsea "legend" despite a painful end to his managerial run at Stamford Bridge.
Tuchel was hired to replace Lampard at Chelsea following his dismissal in January 2021 and the pair will meet for the first time on Sunday.
The Chelsea manager said that Lampard, now in the Goodison Park hotseat, sent him a good luck message when he was appointed.
Aware that he could push Lampard's team closer to relegation with a victory at Goodison, Tuchel was quick to declare his admiration for Lampard.
"He sent me a very kind, respectful message after I took over at Chelsea that meant a lot," Tuchel said.
"I was a huge fan of him as a player and he is and will remain a legend at our club and this is a given. I was very happy when he wrote me that message and it was very gentlemanly."
He added: "I have never met Frank in person. I would love to meet him. We need the points, they need the points urgently as well."
Liverpool 2-0 Everton ratings
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LIVERPOOL RATINGS: Alisson Becker 6 - The Brazilian had little to do but had one nervy moment when he punched the ball into a crowd of players. He earned cheers near the end when he mocked Pickford’s time wasting. Getty -
Trent Alexander-Arnold 5 - Most of Everton’s best work came down the 23-year-old’s side and he was booked for a last-ditch tackle on Gordon. His impact going forward was limited by the massed defence. AFP -
Joel Matip 6 – The 30-year-old had a few difficult situations and was lucky not to give a penalty away when tangling with Gordon. He always looked to get upfield when given space on the ball and was involved in the build-up to the first goal. Getty -
Virgil van Dijk 6 - The Dutchman tangled with Richarlison but came out on top. He is not in peak form but was solid enough. Reuters -
Andrew Robertson 8 - The Scot scored the crucial opening goal and, just as important, cleared a threatening cross from Alli to preserve the lead. He was relentless in his effort. AP -
Naby Keita 5 - The Guinean was unable to impose himself in the midfield war of attrition and his passing was off. He was replaced by Origi in the 60th minute. Reuters -
Fabinho 6 - The Brazilian got on top in the central areas but his probing passes forward rarely carried a threat. He was quick to loose balls. PA -
Thiago 6 - The 31-year-old worked to find the passing lanes but space was hard to find in the congested final third. He pressed and tackled with gusto. AP -
Mohamed Salah 7 - The Egyptian was swamped by defenders but when he found a yard of space he punished the defence and set up the opening goal. AP -
Sadio Mane 5 - The Senegalese got lured into a physical battle and became involved in a couple of pushing matches. He was withdrawn with half an hour left for Diaz. Reuters -
Diogo Jota 5 - The Portuguese found it hard to get on the ball. He drifted out of the game for long periods and was replaced by Henderson with eight minutes to go. EPA -
SUBS: Divock Origi 8 - The Belgian loves playing against Everton. He came on for Keita with half an hour left and helped set up the first goal before scoring the second, his sixth in derbies. PA -
Luis Diaz 7 - The Colombian replaced Mane with 30 minutes remaining. His acrobatic effort gave Origi the opportunity to kill off the game with the second goal. PA -
Jordan Henderson 7 - The 31-year-old came on for Jota to see out the last eight minutes. He provided the cross that led to the second goal. Getty -
EVERTON RATINGS: Jordan Pickford 6 - The 28-year-old made several good saves and his distribution was impressive. There was little he could do about either of the goals. Reuters -
Seamus Coleman 5 - The Irishman put in a battling performance and gave Jota little leeway. He was worn down as the game went on. EPA -
Mason Holgate 6 - The 25-year-old produced a series of blocks and clearances. He remained strong as the pressure built. Reuters -
Michael Keane 4 - The 29-year-old was drafted into the side after a pre-match injury to Godfrey. It was one of his better displays but he was weary towards the end and switched off on the second goal. Getty -
Vitaliy Mykolenko 5 - The Ukrainian did well against Salah but all the good work was spoiled when the striker found a yard of space and created the opening goal. Reuters -
Allan 5 - The Brazilian sat deep to protect the defence and showed little going forward. He was replaced by Alli in the 73rd minute after the team fell behind. Getty -
Abdoulaye Doucoure 4 - The 29-year-old worked to disrupt Liverpool’s momentum but could not exert any control in the central areas. His use of the ball was poor. Reuters -
Alex Iwobi 5 - The 25-year-old played in a withdrawn role that did not suit him. He tried to break quickly but rarely worried the opposition. Reuters -
Demarai Gray 5 - The 25-year-old went close with a shot but was often too busy defending to express himself. He needed to be more ambitious when his team went behind. AP -
Anthony Gordon 7 - The 21-year-old ran at the defence and got into the space behind Alexander-Arnold. He should have been awarded a penalty after a clumsy challenge by Matip. Everton’s best player by far. Getty -
Richarlison 5 - The Brazilian has an inflated idea of his own status and would be better showing off his talent – which he has in abundance – than getting involved in niggle. He worried the defence less than he should have. AFP -
SUBS: Dele Alli 5 - The 26-year-old joined the action for Allan in the 73rd minute. He found space down the right and his cross created one of Everton’s most dangerous moments. On the downside, his defending was poor on the second goal. Reuters -
Salomon Rondon 5 - The Venezuelan entered the fray in the 77th minute for Gray. There was not much he could do because the game had got away from Everton. AP
