Everton flirted with relegation for much of last season, only securing safety in the penultimate game of the campaign with a 3-2 comeback win over Crystal Palace at Goodison Park.
The Toffees also suffered a 2-0 loss to Arsenal in their first pre-season game last week.
Lampard has not been enthused with what he has seen so far and sounded a warning to his players about the challenges they faced last season.
"The players have to understand that we were in a relegation battle for a big portion of last season," the head coach told reporters after his side's loss at Allianz Field.
"We had an amazing night [against Palace] and an amazing run which was great historically for the club but, as soon as that finished, I put it to bed very quickly so the players better put it to bed as well.
"We were in that fight for a reason and, if we don't want to be in that situation again, they have to be better, I have to be better."
Lampard added: "Lots to think about, lots of work to do. What matters is where we are at in two and a half weeks.
"If there is to be good to come out of this, the players and the dressing room have to understand that they have just put in a very poor performance individually and collectively and been well beaten."
Everton begin their 2022/2023 Premier League campaign at home to Lampard's former club Chelsea on August 6.
