Coventry backed up their victory at Nottingham Forest before the international break, scoring four goals in the top flight for the first time since a 4-1 win over Sheffield Wednesday in May 2000.
Those around the Sky Blues' training ground at Ryton feel that, if they are competitive over the next seven games, they will have a platform for survival.
A trip to Tottenham and the visit of Fulham - both winless - come next, with games against Sunderland, Everton, Crystal Palace, Leeds and Ipswich to take them into December.
"It's big and we have to tap into that in a good way, in a humble way," said Lampard, whose side are now 14th.
"We have to be excited and I'm seeing players in my eyes that are developing quite quickly.
"A lot of players had low Premier League minutes, or zero Premier League minutes - Jack Rudoni, [Brandon] Thomas Asante, [Ephron] Mason-Clark, a lot of them.
"So is it human nature in the first few games we've had two top teams in the league (Arsenal and Manchester City) and we've had Brighton and we've gone: 'hmm, it's not easy here'.
"This [win] gives good confidence, so it's the balance of confidence against overconfidence. But it's great when you have a template of feeling when you get a result of that level."
It can be a defining six weeks for Lampard's men after a resounding, if not perfect, win against Newcastle.
Coventry's previous home games had seen them fall to a 1-0 defeat by fellow promoted side Hull before a 5-0 thumping by Brighton.
Sandwiched in the middle was a 3-1 loss to Aston Villa in the Carabao Cup, meaning it was imperative they found form at the CBS Arena.
"We're going to be a relative underdog in pretty much every game," added Lampard. "So we have to maximise everything and be on the limit and I thought we were on the limit in loads of ways.
"They need to keep their feet on the ground because the next one's tough and the one after that will be tough.
"But we look like a team that [will make it] hard for teams to come here. That's the feeling we haven't quite had in our first CBS games this season."
Lampard handed a first Premier League start to Cherif after his summer move from Fenerbahce and the teenager repaid the faith.
"We've got a lot of belief in Sidi, a big signing for the club," said Lampard, after inflicting a second successive 4-1 away defeat for the Magpies.
"He's very respectful but there's a hunger that flicks on when he goes on to the training pitch and in game. I felt it from our first meeting and I've seen it in training, he wants to train and do well.
"Sometimes you don't realise he's 19. He'll be disappointed with the one he missed and I've said to him it's no problem because that's good. You get there, you get hungry, you go again. He's got that little edge to him in a good way."
At 19 years and 301 days old, Cherif is Coventry's youngest Premier League goalscorer since Robbie Keane against Middlesbrough in April 2000 (19y 282d).
He is also the first player to score a Premier League goal from outside the box for the Sky Blues since David Thompson struck against Newcastle in January 2001.
His crisp finish, though a forest of defenders, was a first in his fourth appearance for Coventry, having already won the early penalty.
Coventry scored 97 goals as they won the Championship last season and the ruthless nature of their finishing was a reminder of their striking power.
With Hadji Wright still out with a serious thigh injury, much of the goalscoring burden will fall on £20m Cherif, who was not even born the last time Coventry were in the Premier League.
Lampard said: "Sidi has played in European competition with Fenerbahce, so there is something about him that hopefully feels like he belongs on the level.
"There's something about him I think is a bit special."