McLaren racked up 367 laps with the new MCL36 car during the test, trailing only Ferrari and Mercedes for mileage.
Mercedes driver George Russell said on Thursday and Friday in Spain that he thought McLaren looked competitive, calling the team “incredibly strong”.
While Norris said it was a “decent start” by McLaren, he said it had been far from perfect for the team as it battled various issues through testing.
“George obviously topped the timesheet, so if he thinks we're strong, we’re going to think he's strong,” Norris said after Friday’s morning session.
“But if there's any team on the grid right now that you'll expect to be at the front when it matters, it's got to be Mercedes and probably Red Bull.
“So no, I don't think we're in an amazing place. I think we're in a good place. We had a car which as soon as you put on the track, worked well. Of course, there's always new things and some unexpected issues here and there. But it's been a good start.”
There were no red flags or stoppages on the opening day in Barcelona, but more reliability issues began to emerge across teams as the test continued, resulting in five red flags on the final day.
One of the biggest challenges facing teams through testing has been a porpoising phenomenon with its cars, caused by the new ground effect aerodynamic requirements, which McLaren appears to have got on top of quicker than other teams.
Asked if he was surprised by the level of reliability in the first test, Norris said: “No, I don't expect bad things to happen. You work at the highest level.
“But we still had a lot of issues. It's not been perfect. Maybe from the outside it looked amazing. But still many things behind the scenes, which were not out of control but just to work on and fix and we'll amend for the future.
“I think it was as expected. We've had our issues. I think a lot of other teams have had their issues as well.
“I was just trying to iron them out and make sure they didn't happen either the following days or into the next test.”
Norris will get his next chance to drive the McLaren MCL36 at the second F1 pre-season test in Bahrain, running from 10-12 March, ahead of the season-opening Bahrain Grand Prix on 20 March.