Piastri was running second behind race leader Max Verstappen in the early stages at the Hungaroring when at the first stops the team elected to pit third-placed Norris.
The extra pace that Norris got from fresh rubber was enough to help him leapfrog Piastri, who stopped one lap later and found himself emerging from the pits behind his team-mate.
While the decision to pit the second car was slightly unusual, because teams normally give the better option to their lead car, McLaren team principal Andrea Stella has explained the reasoning behind its decision.
He said that the team chose to stop Norris first because there was a risk of him getting undercut by Lewis Hamilton behind him, so it was better for the team to stop the Briton first.
McLaren also was not anticipating that Norris' pace on fresh rubber would be enough to overhaul Piastri, who had looked solid in the first stint.
"In terms of the undercut that we had at the first stop, you just go really with the sequence that is natural, because you cover with the car that is more at risk, and then you cover with the other car," explained Stella.
"Lando's out-lap was just super, super quick, which meant Oscar lost the position. To be honest, our approach to these situations is to think about the team first. We think as a team, and then we deal with the internal situation."
Stella cited the example of Ferrari's strategy blunder at last year's Hungarian Grand Prix, when the team put Charles Leclerc on slower hard tyres because it felt threatened by Verstappen, as an example of teams needing to be mindful of external factors.
"I think when you are fighting against other competitors outside your team, you need to be very careful that you don't engage in an internal battle that will cost the team," he said.
"I think I mentioned already that if we see last year's race, maybe that's what happened with the red car. And it was very expensive. So, we want to stay away from that."
The strategy call that moved Norris ahead ultimately proved insignificant because Piastri's pace fell away dramatically in the second half of the race, and he eventually came home in fifth place.
Stella revealed that the Australian was hampered by floor damage, which cost him rear downforce.
"Oscar had damage on his car, and this meant that he lost some time from a performance point of view," he said.
"But also, we think because this was rear downforce, I think this caused extra degradation of the tyres. And that's part of the reason why he struggled then to keep up with Lando, but also with the other cars coming behind him."
McLaren suspects the kerb damage was picked up by Piastri after running over a kerb.
