Lampard’s side were on a six-match unbeaten run before they lost to Manchester United 2-1 on Sunday at Goodison Park.
Everton have 10 points from their opening nine games, and their next two Premier League fixtures will be away from Goodison Park, taking on Tottenham Hotspur and Newcastle United.
Lampard is of the view that critics will doubt their chances against top opponents in Spurs and Newcastle and consider them the underdogs going to those fixtures, but he believes his side to be more than capable of proving the naysayers wrong.
The Everton manager emphasised that there are no easy runs of fixtures in the Premier League and insisted that the only appropriate response to criticism is to disprove the critics.
When asked about the upcoming tough fixtures against Tottenham and Newcastle, Lampard said at a press conference: “You could say that about every run.”
“There are no easy questions to answer, other than that the Premier League will always throw up difficulties.
“People probably make us underdogs in both of these games because we are away against strong teams.
“Let’s enjoy it.
“We have shown things already this season that we can go against people’s opinions of us.
“I heard a lot of opinions before this season that we were going down and I was number one to be leaving.
“There is nothing better than proving people wrong.”
Last time Lampard’s side visited the Tottenham Hotspur Stadium in March they suffered a 5-0 defeat at the hands of Antonio Conte’s side.