The loss on Saturday evening was a first in 10 league games for Lampard’s side and will be seen as a missed opportunity to go top of the Premier League table.
And while Lampard didn’t go as far as to say his side lacked desire, he certainly believes they should have been much better.
“We were not at our best. The first 20 minutes or so were key for me,” he told BT Sport.
“I knew it was coming, some longer balls and second balls from a team that are desperate for a win and capabilities to make things very difficult. We found that out last year.
“We hit the post twice and you could maybe argue that we could have got a draw out of it but for our levels and what we’ve been at recently it wasn’t good enough.”
"I would not say energy or desire wasn't there, we were just off it. The lads are gutted because we were on a good run.
"If they are going to make it difficult for you, don't concede from a long ball, second ball situation. We have been getting down the sides, the quality of crosses has been good and it wasn't today. Credit to Everton."