Balotelli, 20, stepped off the bench to score the winner in the 1-0 play-off first leg victory against Timisoara in Romania. He swept the ball home from close range after being set up by Emmanuel Adebayor in the 72nd minute.
It has been a whirlwind week for Balotelli, whose registration was only received by UEFA on deadline day after he arrived last week from Inter Milan for a reported £24 million.
"He had a great debut and I am happy that he scored," Mancini said. "He is a good player. He needs to improve of course and get to know everybody. It was the first time he had played with the team.''
Balotelli, however, picked up a booking after losing his cool and was told by Mancini not to repeat his actions in England.
"We must work on this with him because it will be different in the Premier League than in Italy," Mancini warned.
Balotelli needed treatment at the end of the game but should be available to face Liverpool at home on Monday. Mancini said: "We do not think it is serious. It was probably just a kick, it is not a problem."
England's biggest spenders were good value for their victory after stepping up the pace in the second half. Yaya Toure thumped a shot against the post before Balotelli stunned the industrious home side.
"It was a difficult game because Timisoara are a good team and they played very well in the first half," Mancini said. "In the end, it is a good result for us. But they made it difficult for us by getting so many players behind the ball.
"All the players played well, especially in the second half and we moved the ball quickly. When (Adam) Johnson came on, he also did well. I think we deserved to score another goal because we had three or four good chances.''
But Mancini stressed that the tie was not over and there was still work to be done at Eastlands, adding: "Football is strange. When you think you can win easy, you must have maximum concentration.''