Having been in the mix in qualifying in the chasing pack behind the dominant Red Bull of Max Verstappen, Norris finished sixth and team-mate Oscar Piastri eighth following a race-long fight with Mercedes duo George Russell and Lewis Hamilton.
It was a largely expected result for the Woking squad, which is miles ahead of where it was at the same venue 12 months ago, but isn't yet in the position to scale the heights of its impressive second half of 2023 either.
Bahrain further confirmed that the low-speed weakness carried over on its recent cars still hasn't fully been addressed in the MCL38, which continues making Sakhir a tough circuit for Norris and Piastri to tame.
"It's no different to last year," Norris said. "Those things we've not been able to tackle, other things which make us so up and down every weekend.
"It's something I think that made us struggle so much today and the wind changed. Some corners just felt shockingly bad compared to yesterday.
"I think it's clear there are still a lot of areas we need to focus on if we want to be more consistent and challenge.
"But considering it's a track we struggle with still, the fact we're so close to Mercedes is still a good sign for us that at some tracks we'll be able to be ahead. I'm confident, the team is doing a good job and it's a good starting position."
Norris finished under two seconds behind Russell, whose race pace was compromised by engine overheating issues, but struggled to challenge the Mercedes in its turbulent wake.
"We were close to Mercedes, I don't think we had any advantage over them," he added. "The pace was so similar that, as soon as I got into the dirty air, I didn't have enough of an advantage to have a chance to overtake or even get within DRS.
"Maybe I could have been ahead of George, but that's about it. I think we're where we expect it to be and that's just a good start to the season, so I'm happy with that."
Asked if Saudi Arabia's fast and flowing Jeddah Corniche circuit will be more to the MCL38's liking, Norris replied: "Honestly, I don't know. It's a bit more high speed, a bit more medium speed, which normally suits us.
"But it's also a track where you want to have a good front at apex and this is something we don't have at all, so there are still going to be things we're going to struggle with a lot.
"On average, the track speed is higher, which maybe should suit us a bit more, so I'm excited for it."
