Everton were heavily beaten 4-1 at home to Brighton and Hove Albion on Tuesday, leaving them 16th on the table, just one point above the relegation zone.
The Toffees were 4-0 down by the half hour mark and only a fortuitous penalty in stoppage time saw Demarai Gray get them a consolation.
Everton have won just three league games all season and have lost four of their last five games.
The pressure is mounting on Lampard, who was appointed as Rafael Benitez's replacement in January last year, but the former Chelsea boss is adamant he will turn things around.
"Since I have been in here we have been in this situation, so it's not a case of fear, it's a case of just keep working," Lampard told reporters when asked if he feared for his future.
"I can't control the talk or the decisions, when you are around this area of the table this is what happens.
"You lose a game like this, I absolutely understand any reaction. I don't listen to too much of it because if you do then it becomes your focal point, so I don't focus on it.
"I'm very confident in myself and will work to turn it around. I can't predict the future. We have to try and win games — it's all we can look at."
Everton got a creditable 1-1 draw at champions Manchester City over the weekend, and midfielder Alex Iwobi believes a lack of consistency is their main problem.
"I don't think confidence is the issue," Iwobi told Sky Sports. "We showed how we can play against Man City.
"We can't be one minute good one minute bad. We've got to be consistent. The way we discussed in the changing room now is we all want to fix it.
"I'm confident we can get ourselves out of this."
