Norris went off the track at Stavelot in the first half of a wet Q1, skating through the gravel as his race engineer suggested the Briton had sustained front wing damage.
Closer inspection in the garage revealed Norris had significantly damaged his floor, which left him compromised for the rest of the mixed-weather session.
Norris ended up making it into Q3 but had to settle for seventh behind rookie team-mate Piastri, as the McLarens struggled for top speed down the straights.
"I went off in Q1 and completely destroyed the floor, so I'm happy to have made it to Q3 and only be a couple of tenths off what Oscar did," Norris told Sky Sports F1.
"I think he did a good job. His middle sector was very strong. We were very poor in the straights.
"There's wins and losses, but I'm happy. It could have been a lot worse, I could have been out in Q1, so I'll take P7."
When asked to explain how much of his MCL60's floor was damaged, Norris said: "The whole thing. Normally, you can repair it [under parc ferme rules].
"Tape is not going to help. We tried to tape it. They did a good job on getting as much as they can fixed, but too much to be competitive today.
"So, I don't think we're bad. I think if we had a car that was together, if I hadn't made the mistake in Q1, we could have had maybe a slightly better day.
"We weren't miles off the guys ahead, but I'm happy I got what I did out of it."
Piastri also felt he hadn't extracted the maximum performance out of his McLaren.
A rained-out free practice session meant a wet-to-dry Q3 was the only slick-tyre running the 22-year-old debutant was afforded at Spa-Francorchamps, meaning he had few references.
"I felt very comfortable when the conditions were really tricky like that," said the Australian.
"I think in some ways, the track drying up and becoming closer to normal was a hindrance for me because I've not done a dry lap around here in an F1 car.
"So, for braking points and stuff like that, especially when offline, it's wet, you never want to brake too late and I think that's where I left quite a bit on the table, unfortunately."
McLaren excelled in recent races with Norris taking two consecutive podiums in Silverstone and Budapest, its 2023 season reinvigorated by a comprehensive car upgrade.
But according to Piastri, Ferrari, which will start on pole with Charles Leclerc, will pose a bigger threat in the fight for second behind the dominant Red Bulls.
"Ferrari seems stronger this weekend, so it's not just two teams fighting for second best, it's more like three, possibly four.
"We've got another qualifying and the sprint to go but I think we can be confident. The pace and the car are still quite good."
