Stead expressed sympathy for Patel, who has failed to take a wicket in three Tests on home soil, despite his heroics in India.
"You do feel for Ajaz after his record-breaking display in India," he said.
"However, we've always applied a horses-for-courses selection policy and believe the players selected best fit the way we want to take on Bangladesh here at home."
Stead said it was "obviously disappointing" not to have Williamson but the battling stalwart was undergoing comprehensive rehabilitation to fix his troublesome elbow.
"We have every confidence in Tom leading the side, he's done an excellent job in the past when called upon," he said.
New Zealand squad
Tom Latham (captain), Tom Blundell, Devon Conway, Matt Henry, Kyle Jamieson, Daryl Mitchell, Henry Nicholls, Rachin Ravindra, Tim Southee, Ross Taylor, Neil Wagner and Will Young.