The Briton, who is 62 points behind title rival Max Verstappen heading into the weekend, said his team were 0.3-0.4 seconds slower than the front-runners on the Baku track.
Ferrari’s Charles Leclerc set the pace, 0.006secs ahead of Red Bull’s Sergio Perez with Lewis Hamilton’s Mercedes third, 0.066secs off Leclerc.
Norris was 17th fastest after being held up by Alpine’s Pierre Gasly on his fastest lap, but he said team-mate Oscar Piastri’s fifth place, 0.5secs off the pace, was “more where we are”.
“If we nail it we are just about there,” Norris said. “But I’m sure they are not even close to nailing it yet.
“We have quite a lot to find compared to Mercedes, Red Bull and Ferrari. They are all very similar and then there is a good 0.3-0.4secs gap back to us. A lot of work for us to do.”
McLaren said before the race weekend that they would “bias” their support towards Norris and ask Piastri to help if the circumstances arose.
Norris has to close an average of just under eight points a race on Verstappen to beat the Dutchman to the title, which he has done over the last two races in the Netherlands and Italy.
Norris said the low-grip conditions in Baku were working against McLaren.
“We always know that Ferrari are very quick here,” he said. “With these track conditions Mercedes are going be very quick.
“It is very slidey out there. We perform very well in the higher grip circuits naturally and the track is way off where we were last year.
“I’m finding it difficult at the minute but we will work hard tonight. The car is still not bad. I’m sure we can still get a lap time out of it but we are not as clearly ahead as we have been at other races.”
However, despite his bleak assessment, Norris’ lap was a match for Leclerc’s fastest time until he came across Gasly on the final straight.
And Piastri appeared to be among the fastest cars on a race-simulation run on heavy fuel later in the session.
Leclerc quick as usual in Baku
Leclerc’s fastest time, set when the track was in the region of 0.3-0.4secs faster than it had been when Perez did his, came after an incident-filled day for the Monegasque, who has been on pole in Baku for the last three years.
He crashed midway through the first session, and then ran into a technical problem at the start of the second session, which curtailed his running time.
When Leclerc first said there was a problem after taking to the track, the team told him they could not see any issues on the telemetry. But he said the car felt “not straight” and he needed to come in to the pits, saying: “It’s impossible you cannot see that on the data.”
After the session, Leclerc said: “When we started P2 there was a problem on the car which we saw late on once I stopped (in the pits) and we we changed that particular part,” he said.
“It was nothing to do with the crash, we just had a problem with one new part we had just put on the car but that was giving me a very strange feeling with the steering wheel, changed that and then it was fine, not as many laps as I would have hoped for but competitive anyway.
“It is very tight but it is very difficult to see (the true competitive order) with different engine modes for everybody.
“We have been pretty quick in the past but it doesn’t mean it will be the case tomorrow. There is quite a but to improve and with my driving, but we are fast and hopefully more to come.”
Red Bull make improvement
Mercedes have removed an updated floor introduced a couple of races ago and looked more competitive than they did in the last two races – Hamilton said he had had a “good day”.
And a new floor on the Red Bull seemed to have put them in more competitive shape than they were on a difficult weekend in Italy, when Verstappen qualified seventh and finished sixth.
Verstappen was fastest of all in the first session but complained of understeer in the second, in which he had a near miss with the wall and a trip into a run-off area.
He ended up 0.545secs off the pace but said: “Overall a good day, we learned quite a bit, now it is just about tidying up the things we tried, so far we have been more competitive this weekend, so that’s positive.”
George Russell was another to have a difficult session. He was late out after Mercedes discovered a problem that required an engine change and then was called in before the end of the session with a sensor problem – the team thought they had a water leak but they did not.
Russell ended up ninth fastest admitting that on top of the reliability problems he was “struggling – I was definitely off the pace compared to Lewis, struggling with confidence in the car and trying to get the set-up in the right window”.
Oliver Bearman, standing in for the suspended Kevin Magnussen at Haas, was 10th fastest, two places and 0.072secs behind team-mate Nico Hulkenberg.
“It was nice how it ended up, I was confident in the car, which is really important on a track like this,” he said.