Norris headed the Q2 times on medium tyres, as F1 rolled out a new 'alternative tyre allocation' trial that stipulated which compounds teams must run in each qualifying segment, but came up just short in Q3 following the switch to the soft rubber.
The Briton was denied a second career F1 pole as he clocked a 1m16.694s that was just 0.085s slower than pacesetter Lewis Hamilton's Mercedes, who pipped Max Verstappen's Red Bull by 0.003s to end a pole drought dating back to Jeddah 2021.
Speaking after the session, Norris acknowledged that he was "a little bit" surprised to show so well in Hungary, before conceding his frustration.
"I'm disappointed, I guess," he said.
"If you're doing within a tenth of pole, it feels like you should be on pole if you put the lap together."
On a strong day for McLaren, following on from the British Grand Prix last time out where Norris and Oscar Piastri started second and third, the papaya team locked out the second row with Piastri lining up fourth.
But Norris admitted to making "too many mistakes" to be totally satisfied with his performance.
Source: Autosport