Fans were left scratching their heads when Mumbai, under new captain Hardik Pandya after he replaced Rohit Sharma this year, opted to take Indian paceman Bumrah out of the attack after he bowled the fourth over on Wednesday.
Bumrah returned in the 13th over, by which time Hyderabad had made 173-3. Klaasen went on a late onslaught to score 80 off 34 balls while Aiden Markram hit 42 off 28 balls.
With Travis Head earlier scoring 62 and Abhishek Sharma putting up 63 Hyderabad finished 277-3 in 20 overs.
Mumbai pushed hard in reply but lost the game by 31 runs, posting 246-5.
"They didn't bowl their best bowler in the powerplay ... that was our plan," Klaasen told the official broadcaster.
"They missed a trick up front. We've got incredible strikers up front in our batting line-up. They just set the tempo, so our work was basically done."
Bumrah finished 0-36 in four overs of work.
Former Sunrisers coach Tom Moody echoed South African Klaasen's views while analysing the game for ESPNcricinfo.
"I totally get if they want to use a couple of swing bowling options in the first or second over," the Australian said. "But Bumrah has to bowl two overs in the powerplay because of what he brings to the table.
"One of the priorities in powerplay is wickets and he's your best wicket-taker. He always will be. For him and Mumbai to be starved of that opportunity to try and stem the flow of this onslaught is crazy.
"It doesn't seem right."
