Sporting a bold, new design for its RB20, F1's dominant force Red Bull impressed at Sakhir with its consistently-rapid long runs.
Ferrari also caught the eye with a much more balanced and stable SF-24, which appears to have gone some way towards addressing its 2023 race pace struggles, while Charles Leclerc and Carlos Sainz also delivered the headline lap times.
According to Norris, both teams will be well ahead of McLaren at next week's season-opener, even if he feels his squad has made solid progress as well and is starting the year much more on the front foot than it did in recent years.
"Do I think we've taken a step forward? Absolutely," Norris said on Friday. "Do I think we've made a lot of things better? Yes.
"But you just never really know at the end of the day where we stand compared to the others. I think we're in a good position. We had a decent car at the end of last season.
"I think we've definitely taken some steps in the right direction, but I think it's still a very long way behind Red Bull and a long way behind Ferrari. So, plenty of work for us to still try and achieve, but also plenty of things that we've learned over the last few days for us to implement before next week."
McLaren's MCL38 was hit by a spate of minor teething issues which restricted Norris in particular to 145 laps over three days, which is still a reasonable number but fewer tours than most of his peers.
Norris said the issues were "not the end of the world" although he did miss out on some helpful long runs.
"Yes, just a few setbacks here and there over the last few days. Not the end of the world, definitely, but you always want a perfect day.
"We didn't get any long-running high-fuel stuff [Thursday] night, and we moved into [Friday] morning, and we still didn't get it.
"So, not exactly what I wanted, but still plenty of things learned and a lot of stuff that I wanted to get done. I was happy for the most part, but [there are] a couple little things that I wish I could have done more."
