Chris Hogg's side take on their City counterparts at Whitley Park (kick-off 1pm GMT) and bid to record succesive home wins following a 4-3 win against Leeds United over a fortnight ago.
Brookwell, who joined the Magpies last summer following his departure from Liverpool, is expecting a tough test against Norwich who currently occupy third place in Division Two.
The Wigan-born midfielder told nufc.co.uk: "I think it'll be a good game, no matter how early it is in the season. They are near the top of the table and there's a reason why they'll be there. They'll be a good team.
"We know if we bring everything together and do what we've been doing this season in moments, we can beat them.
"We are aware of the positions in the table. We try and focus on our performances and then we know that the results will come. It's tight in the league and with one win, it can take you up the table so that's what we'll be looking to do."
United's second-string were involved in Papa John's Trophy action on Tuesday night, suffering a disappointing 3-2 defeat against Bolton Wanderers despite taking a two-goal lead at the University of Bolton Stadium.
Brookwell, however, took plenty of positives from the cup clash against the League Two outfit and admitted the defeat only motivated the central midfielder to attempt bouncing back in a strong manner.
The 18-year-old added: "We were disappointed with the result against Bolton although, for the majority of the game, we were happy with our performance. We just need to get that cutting edge and starting killing games off with another goal or making sure we don't concede.
"We could say we were unfortunate but we only had ourselves to blame and why we didn't win the game.
"We were happy with how we played and we competed well. We stuck together and gave it a good go but we'll learn from it and just need to take that going into our next few games."
Newcastle's youngsters currently sit in ninth place but a victory against City could maintain the young Magpies' push for promotion and propel them up the league ladders.
Brookwell is eager for a successful debut campaign and believes the club are more than capable of qualifying for the play-offs or beyond.
"We want to finish as high as we can in the league, whether that is in the play-offs or automatically," the teenager said.
"We all want to get the best out of every game and we feel if we do give our all and produce what we know we can produce, we can definitely be up there.
"I think we need to start getting a bit of consistency with the wins. We need to keep going when we get a win, making sure we don't take our feet of the gas.
"We have lost against sides that we feel we should have beaten. We have had some good results so far this season but we need to get more of them.
"All the lads get along really well with each other, we're working hard and it's showing at certain times. The more we are all training together, the more you get to know each other and their game which can only be a good thing."
