A harsh 1-0 defeat at home to leaders Manchester City left his side one place and one point off the bottom three, although they have games in hand on the three teams immediately above them.
Despite a determined defensive effort, Everton were undone by a mistake which saw Michael Keane miss a deflected cross in the six-yard area to allow Phil Foden to score in the 82nd minute and then were denied a penalty when VAR ruled there was insufficient evidence to penalise Rodri for a handball.
After taking just nine points from the last 54 available, the pressure is really on but with 14 matches remaining to pull themselves out of trouble Lampard is confident survival can be assured.
Their 22 points from 24 league games is their lowest tally at this stage since 1929-30, when the Toffees were relegated from the top flight.
“If the table doesn’t look great in a couple of weeks, so be it,” he said.
“It didn’t look great when I came but I have seen big improvements in performances, confidence and how the club is joined from top to bottom – with fans, players and owners.
“Don’t look too much at the table for the next few weeks. I am not buying time with that… we have a lot of points to play for.
“If we play with the energy and passion we did (against City), my feeling is we will be fine.
“I thought we deserved a point on performance alone – and it doesn’t always work like that – but when you play against City, you understand how the game might go; possession against you, having to defend, press, cover and do a lot of work.
“And we did it brilliantly, from first minute to last.
“The performance was great, the organisation and work ethic we wanted was applied by the team.
“Every player, for their application, for their bravery on the ball… I am very proud and on reflection we will look back and think, ‘What a performance’.”
Lampard was boosted by the return of influential midfielder Abdoulaye Doucoure after more than a month out with a groin problem.
The Frenchman played somewhat surprisingly played the full 90 minutes but that was testament to his overall performance.
“He was incredible. I was a big admirer before I came, so to have him injured was disappointing,” added the Everton manager.
“To see him produce that level of output and performance against the best team in the league was great.
“It is a big plus to have him back.”