Les Bleus have already qualified for the Champions League next season by finishing quarters in the Premier League, but the Gunners will have to win at Wembley to qualify for the Europa League.
Lampard told BBC Football Focus: “I’ve heard more about this game for Arsenal and I’m worried about that idea.
“We have to put pressure on ourselves. It’s a huge game for Chelsea.”
Lampard and Arsenal’s two opposing numbers, Mikel Arteta, can earn their first control honours at Wembley, and both are on Football Focus from 12:00 BST on Saturday on BBC One.
Although he knows they will be playing at Europe’s elite club festival in 2020-21, Lampard, who has won the FA Cup four times as Chelsea player, says his team will have to feel the strain of delivering trophies at Stamford Bridge.
“I’m concerned that as a club, as a team, we think we achieved something last week by completing among the four most sensitive,” said the 42-year-old former England midfielder.
“We’re satisfied with that, but now we’re out. We don’t know what that means for Arsenal, we have to win the game.”
“I’ve been in this game for a while, but I’ve been betting for many years and I know what I have to feel around a final. We have to work hard, we have to be at the forefront. We can’t sail. In the final, you lose them like this.
“The feeling of waste as a coach is worse than as a player because one takes on more responsibilities, the feeling of winning is better.”
Lampard has shown whether Kepa Arrizabalaga or Willy Caballero will start in goal, but French midfielder N’Golo Kante and Brazilian winger Willian are available.
The final of the 139th FA Cup starts at 17:30 BST on Wembley and can be viewed on BBC One, iPlayer and the BBC Sport website.
This season’s centerpiece has been renamed Heads Up FA Cup Ultimate to raise awareness of intellectual health.