McLaren has decided to give one of their seats to the young 19-year-old Brit meaning that Stoffel Vandoorne was left without a drive.
"Formula 1 can be a pretty cruel environment," the McLaren boss told The Sun.
"We need to manage expectations, not after three races, and pass judgment, which we as a sport are pretty quick to do."
Brown has promised to give Norris time to prove himself.
"He will definitely be given time to develop. It is a high-pressure environment and the first thing anyone does in Formula 1 is compare you to your teammate."
Carlos Sainz will also be driving for McLaren next season.
"We expect them to race each other hard, cleanly and, for sure, they need to get the measure of each other from time to time,"
McLaren will hope that they can start to improve their performances this season.