Chelsea defeated Sheffield United 4-1 on Saturday, their fourth win in a row. The Blues have now gone eight games unbeaten and have lost just once in the league this season – a 2-0 reverse against Liverpool in September.
Lampard admits he is happy with the recent run of form but added that his side must remain humble when attempting to match the consistency of their rivals.
"We have to prove ourselves as the gap has been too big now for the level of consistency with two of the best teams in both world football and in the modern era in the Premier League," Lampard told reporters on Zoom.
"So, we have to understand where we are at and be humble about that. We are in a nice moment this weekend. It is nice for [Sheffield manager] Chris [Wilder] to say we have played well today, so that’s fresh in all our minds.
"Now it is whether we can produce it regularly. That’s the next question of us. I won’t get too carried away."
A title challenge might come sooner than many expected from the Blues, who spent £220 million ($275m) in the summer transfer window but faced bedding in six new players without a pre-season.
Lampard feels that his new players have started to build an understanding with the coaching staff that is seeing results improve.
"I never had a schedule, we lacked a pre-season, we had some injuries and I never set a target of the first one, two or three international breaks," he added.
"I just want to work and get to a good level as soon as I can where I feel I understand what I want, what the staff want and what the players want, to understand each other. That’s never an easy one when you start the process, so I think we are in a good place.
"We may have dropped some points because we are working in real-time in games. That’s by-the-by, a lot of teams will say that this season with the way it has panned out."
Chelsea scored another two goals from set-pieces against Wilder's side on Saturday as Hakim Ziyech's deliveries were met by new defenders Ben Chilwell and Thiago Silva.
Silva became the 14th different player to score for Chelsea this season and it was the sixth goal from attacking set-pieces for the club this season. Lampard said that the skill sets of the new signings has led to increased threat from dead-ball situations.
"Yes, it is something that we worked on last year," he continued. "We weren’t happy that we conceded too many goals from set-pieces in games.
"They are a crucial part of the modern game and they probably always have been but seemingly [more] so now as teams have blocks or plans to stop you [from] scoring. We looked at it over the course of last season.
"The personnel certainly has helped, we are bigger and more aggressive naturally through the personnel in the team earlier in the season. The lads have shown focus through the work we have done earlier on the pitch with them.
"We have spent time on that and there’s a nice mentality about them to be as good as we can be with them. They make the game comfortable even though we played well. It might not have been a comfortable game, so I am very happy with the set-piece goals."