The 47-year-old director, who helmed the film starring Liam Neeson and Pamela Anderson, said he didn't want the laughs to come at the expense of the plot.
"That's a very good question," Schaffer told Collider when asked how he and the crew developed the flick.
"Because now it's been a couple of years since we started, we're iterating so fast and writing a whole first act that gets thrown away, and then the best jokes make their way into new jokes.
"When we were trying to figure it out, I would say we were operating on two tracks at once. One was just brainstorming jokes, set pieces that you don't even know how they'll fit in, but just identifying tropes.
"It was just going, 'Oh, when somebody breaks their cell phone because it's a burner, and now they can't get traced', that's an area where we could do.
"So, there's that pile that's just like, 'God, it'd be so good to get any of that into this movie'."
The Chip 'n Dale: Rescue Rangers director said the team wrote "thousands of jokes that didn't make it in".
"And we broke different stories that weren't the story ultimately," he said.
Schaffer is hopeful of making a sequel to The Naked Gun - which serves as a legacy sequel to the comedy flicks that starred the late Leslie Nielsen - and hopes people go to the cinema and watch the film.
"Everything's on the table. We'll see if people will go see it," he said.
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