The Blues winger bagged a first half hat-trick in the 6-1 win at St Andrews.
"His finishing was so clinical," Rowett said.
"We toyed with him this week about how many goals he's actually scored. He said 'one', and you could see on his face a look of disgust with himself.
"So I'm really pleased for him, he's a young player and we'll keep his feet on the ground and make sure he puts a shift in as well as showing his quality.
"It's our job, to try to get players playing for this club who have come through the system who, ideally, other teams want in their side," Rowett said.
"We've benefited from that today. The pleasing thing about Dimi today was not only his play on the ball but also off it. He was very, very good."