Lampard wants further Everton improvement after toppling West Ham
A goal from new signing Neal Maupay early in the second half settled a contest that sprang to life only after the break as Everton had to weather a West Ham storm after going in front.
But the home side also created enough in the game to have won by a greater margin and Lampard hoped that would be the springboard to improved performances, particularly in attack.
"The reality is we’ve worked hard this season and deserved more," he told SkySports. "To hold on, fight, dig in, we showed a lot of parts. We’ll get better. This team has to be a reflection of the fans.
"The passion of the fans, they demand things and they’d better see them. We have players who can deliver that, characters.
"Hopefully our football can get even better. Nobody is getting carried away. At the moment there's a decent feeling round the place."
Lampard was pleased for Maupay, who arrived from Brighton & Hove Albion in the transfer window and had a number of chances to score on debut in the goalless Merseyside Derby last time out.
"He's a proven Premier League scorer. We played some games early season with false nines, trying to find solutions," Lampard said.
"There were times in games with that bit of clinical finishing, we would have got more points. How close he kept that first touch and how quickly he shot is why he scored.
"You can see we’ve added a lot in the dressing room. We have to be hard to beat."
Everton are next in action after the international break, away at Southampton on October 1st in the Premier League.