The Blues jumped out of the relegation zone with a 2-1 win against Leicester on Sunday at the expense of Leeds United, whose failure to get a result against Arsenal at the Emirates caused them to drop into 18th place.
The Merseyside club now sit 16th, one point ahead and one game behind both the Whites and 17th-placed Burnley.
On Wednesday, Everton travel to Vicarage Road to contest their game in hand against already-relegated Watford.
Lampard is insistent that his players stay focussed as there is work yet to do to secure Everton's Premier League status.
"The only message for us is that as much as we enjoyed the weekend - it was a game that got us out of a relegation zone with games to go - it's very dangerous now to relax on that," Lampard said in his pre-match press conference.
"So as much as we can talk about the fans, and the great atmosphere, us - as players and staff - the only message is that we have to go and now finish the job, which is a tough job.
"We have to expect the worst everywhere else everyone else can win.
"But we can control ourselves, so there's absolutely no way we we can relax - that's the biggest message."
On paper, Watford present a significantly easier challenge than both Leeds' and Burnley's next fixtures, as the Hornets have lost all five of their last Premier League games and have nothing left to fight for.
But Lampard is wary of underestimating the Hertfordshire side, who may perform better now that their fate has been sealed.
"I think pressure is a funny thing," Lampard said. "It can affect you to when you're under it in a negative way to react in a good or bad way. The same when you relieve that pressure. So we'll find that out. But again, focusing on ourselves is the important thing."
Everton will be without three key players when they travel south on Wednesday with Yerry Mina joining Donny van de Beek and Ben Godfrey in the treatment room.
The Colombian, only recently returned from a hamstring injury, picked up a calf issue at the King Power Stadium on Sunday in a big blow for Everton as the Premier League season enters its final phase.
Meanwhile Vitaliy Mykolenko, also a concern in the Foxes win, is fit to face Watford.
"Myko's good. Mykolenko has cramp in the calves, so he'll be good," Lampard said.
"Yerry's not. He's got a small injury in his calf so he won't be playing this game. We're probably looking now towards the last game that Yerry could be in contention for.
"Donny [van de Beek] is not ready. We hope that he'll be ready for next week's games, potentially the weekend.
"Similarly with Ben, he's working with every ounce of sweat and bone in his body to be fit and take part in the run-in. And that's the sort of attitude we need."