Lampard’s side are one point above the bottom three following a 3-2 loss at relegation rivals Burnley on Wednesday.
They have won just twice in nine league games under the former Chelsea boss.
“I know the rules. In my relatively short managerial career I spent 18 months at Chelsea where I was probably two games from the sack,” Lampard said.
“Maybe that’s a symptom of football in the Premier League. That’s pressure, that’s fine, you sign up for that.
“I have no problem with that in terms of speculation. We are a huge club, people want to talk about it. I don’t waste my time, I just do my job.”
Everton are one of six ever-present teams who have never been relegated from the Premier League.
They last dropped out of the top flight of English football in 1951, but with nine games of the 2021-22 campaign remaining their Premier League status is under serious threat.
Lampard has won four games and lost eight across all competitions since replacing the sacked Rafael Benitez at the end of January, with Manchester United up next at Goodison Park in Saturday’s early kick-off (12:30 GMT).
“The fans have a passion, they live and breathe this club. I’m here for five minutes in football terms and I live and breathe the club and I want us to stay in the league,” Lampard said.
“I have to handle that because I have to do my job and I can’t tell the fans how to be, I can only ask them to turn up tomorrow and be absolutely behind us – as they have done since I’ve been here.
“Results are the turning point of things. If we win on Wednesday [it’s a] seven-point buffer to Burnley, six points to Watford with a game in hand. If you don’t it flips in the other direction.
“If we get caught up in that hysteria we are caught up in it. We have a job to do tomorrow.”