The Everton boss and his players were berated and subjected to jeers from their travelling fans after slumping to a 3-0 defeat at Bournemouth on Saturday.
Marcus Tavernier capitalised on a Jordan Pickford error to open the scoring for the home side, with goals from Kieffer Moore and Jaidon Anthony wrapping up the victory.
The Toffees are now just one point clear of the Premier League drop zone with Lampard severely under pressure, but the manager, who believes his side were already written off by many ahead of the season, was keen to stress that things can change very quickly.
"The fact that we're in a relegation battle - I think everyone put us in a relegation battle, it's all I read pre-season," Lampard said.
"It was like 'Everton are in this battle', I was favourite to be sacked, five managers have gone but that's the nature of the beast of what we're working in.
"But we just have to keep our heads down and keep working and try and show reasons where we can amass points, because the picture changes quickly.
"Two weeks ago, we're sitting there and people are talking about top half of the table, now people are looking down at us.
"So I'm the first one that's got to stay pretty stable."
Following their precarious position in the table and the reaction of the fans at the final whistle at the Vitality Stadium, Lampard believes the sizeable break brought about by the Qatar World Cup could be beneficial.
"The fact of not having a tight turnaround is not the worst thing, it's a good moment to reflect on what's been good and what's been not so good and why and how we want to get there," he said.
"So, it will maybe be a good chance to get some more clarity on those points as well."
Bournemouth ended a run of four successive league defeats with the win over the Toffees, who they also defeated 4-1 in the Carabao Cup in midweek.
Interim boss Gary O'Neil would not be drawn over his future at Bournemouth as incoming owner Bill Foley finalises his purchase of the club, but was proud of how the team had performed so far under his tenure.
The Cherries go into the World Cup break in 14th spot with 16 points, three above the drop zone.
"I think they've given me that (everything) in every game so to be honest I don't think today (against Everton) was any different," said O'Neil, who has been in caretaker charge since the 9-0 thrashing at Liverpool in August.
"I think we were very good with the ball, good without the ball, well organised.
"The lads showed heart and determination, we spoke before the game about getting to 16 points by the break and it being massive for everybody involved and the lads deserve at least 16 points for what they've put in in my spell. I think they've been incredible."