Marco Silva refused to discuss his future after Liverpool piled the pressure on the under-fire Everton manager with a 5-2 victory at Anfield.
Silva was pushed to the brink as the Toffees were routed by their neighbours in a one-sided Merseyside derby to slip into the bottom three of the Premier League.
It was Everton's third successive defeat and an eighth in 11 games, leaving Silva under severe pressure and facing the sack.
Silva said: "I am not the right person to talk to you about the situation. I cannot answer to you.
"Since I joined the club and until the last day I am here I will always be 100 percent professional, giving my best every single day.
"I understand why the questions are coming. If we are winning all the games, you are not asking them.
"But it is not for me to take those situations. I don't like to talk after every single match about my future."
Interestingly, Silva's predecessor Ronald Koeman was sacked after a 5-2 loss to Arsenal in October 2017 dropped them into the relegation zone.
On this occasion, Everton were under pressure from the outset as leaders Liverpool, despite naming Mohamed Salah, Roberto Firmino and Jordan Henderson on the bench, started strongly.
Two goals from Divock Origi and further strikes from Xherdan Shaqiri and Sadio Mane put them in command in the first half, even though Michael Keane and Richarlison struck back against the run of play.
The second half was less fluid affair but Georginio Wijnaldum added a fifth for Liverpool late on.
Silva said: "It was a bad game for us, a really bad night. They deserved the three points, no doubt. We were not good enough.
"Always they arrived quicker than us. The way we conceded the goals was not good enough. We should do better, be more brave and win some challenges.
"Last season we finished with the fourth-best defence in Premier League. It was not enough what we did tonight."
While the misery continued for Everton, it was another fine night for Liverpool, who retained their eight-point lead at the top of the table.
The victory also established a new club top-flight record of 32 games unbeaten and was Jurgen Klopp's 100th Premier League in. Coming in his 159th fixture, that was also a new club top-flight record.
Klopp said: "It was really good, especially in the circumstances created by myself with the line-up. Changes can lead to some problems but I didn't see any of them.
"We have to make changes, that is clear. What was clear was it was a really intense game so we needed as many fresh legs as we could get. What the boys made of this difficult game was exceptional."
When it came to his own landmark, Klopp diverted praise to his players but said thoughts were already turning to Saturday's clash with Bournemouth.
He said: "The boys are the reason for the wins but three is the next number when we play against Bournemouth.
"They are not happy with their situation, they want to strike back. So, we have to be ready for that. That is the only thing I am really thinking about."
