The highly touted freshman had 17 points, six rebounds and five assists in his collegiate debut and No. 3 Memphis beat Tennessee-Martin 102-71 on Monday
Calipari said Rose might be the player Memphis needs this year to push them into the Final Four.
"You need to have a guy, that when the game is on the line, he can just dog the other guys and do whatever he wants when he wants," Calipari said. "He can do that."
Memphis senior forward Joey Dorsey has a sprained right shoulder sprain and did not play. He is also expected to miss Tuesday night's game with the injury. Shawn Taggart, a transfer from Iowa State, started in his place and finished with 15 rebounds.
The Tigers will play Richmond, which beat Maine 44-42 on Monday, in the regional final Tuesday night. The winner will play in the semifinals at Madison Square Garden on Nov. 15.