The Briton was beaten to the front row of the grid by rookie team-mate Piastri by a scant 0.035s, although Max Verstappen's advantage over the Australian spanned over half a second en route to pole position.
Norris explained that McLaren would "try" to take the fight to Verstappen, but deadpanned that there was not a lot that the team could do unless Piastri resorted to more nefarious tactics to open the path ahead.
He cited the infamous 1990 clash between Ayrton Senna and Alain Prost at the same venue, in which Senna refused to yield the inside line while behind Prost at the start which caused a first-corner collision that secured the Brazilian the world title.
"We're going to try [to beat Verstappen], but if he's leading by Turn 2, there's not a lot you can really do," Norris said.
"If you want to emulate Senna ['s move on Prost], Oscar, into Turn 1 and do that happily, it would be lovely for me!
"We'll try, I think our race pace is decent, it's definitely not going to be as good as the Red Bull, but we'll do our best."
Piastri added that McLaren would be aiming to provide a similar challenge at the start as it managed at the British Grand Prix, where Norris snatched the lead in the first corner and led for a handful of laps.
The rookie had also challenged Verstappen into the opening corner in that race, but cited that a repeat may be more tricky.
"I mean, we tried our best in Silverstone so we'll try and do the same thing, but obviously it's going to be difficult," he explained.
"I think it's going to be a very difficult race tomorrow as well, very different to Silverstone in that regard. It could be a lot more open."
In a more serious assessment of McLaren's fortunes in Sunday's race, Norris explained that Mercedes may yet offer a challenge owing to its greater performance in the races relative to qualifying, but that McLaren had been strong in its practice simulations.
He felt that the expected high degradation in the race meant there would be plenty of strategy options, citing that the undercut may be powerful.
"I think from the knowledge of our general pace and competitor pace, Mercedes are always very strong on a Sunday. But I think we've been strong all weekend from quali runs and also high fuel runs,” he said.
"We're hoping for probably an easy race, but it's never going to be an easy race around here. Just with undercut power and things like that, I'm sure there's going to be a lot going on.”
