The Briton finished 11th in FP1 on Friday, which he says was "probably one of our worst FP1s of the season in terms of pace," before going on to finish 14th in FP2.
He improved to 10th in a rain-hit FP3 on Saturday morning before finishing third in qualifying, despite saying he "wouldn't say we felt anywhere near this good."
Asked whether he was surprised by the result, Norris said: "I would say, yeah. After FP1 we said it was probably one of our worst FP1s of the season in terms of pace. So to be sat here today, I think it's quite a big surprise for all of us.
"I think the cooler conditions, things just started to come our way a little bit.
"So yeah, it just feels a bit odd, I definitely wasn't thinking at all to be in the top three today, but I'm very happy to be here, so a good day."
He added: "I'm shocked to be here. We've not really brought anything to the car this weekend, the last upgrade we had was Baku with the floor and even that didn't give us a lot of performance, just a different direction to go in.
"We've not really brought too many big things, just some very small things that obviously help a little bit.
"In a good way, I'm happy, but we didn't really change anything this weekend, it's the same car that we've been struggling with, so managed to see some good points from it."
Source: Autosport