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Kirsten had decided to quit from his position as India coach before the World Cup had begun and has played a key role in transforming the Indian team into world beaters.
"Personally I want Gary to continue but I understand he has got commitments and he must have thought about this before the tournament. I respect his decision," Tendulkar said.
"It has been a pleasure to work with him, he worked as hard as the players, he is like a bowling machine, bowling 200-300 balls to the batsmen. It has always been a fabulous experience to rub shoulder with him, we will miss him," he added.
Yuvraj, who was going through a rough patch before the World Cup, said Kirsten was a father figure and helped him to regain his confidence.
"He always kept a check on me. He pulled me up when the chips were down. He is a father figure and I am going to miss him," Yuvraj told ICC`s official website.
Kirsten, under whose guidance India became the number one Test and ODI side, ended with the team`s World Cup title triumph and he has already ruled out reconsidering the decision.
"Cricket has been in the right direction since Gary came on and I hope it will remain so," said Yuvraj.
The dashing left-hander, who was named Man of the Tournament for a fine show with both bat and ball, said winning the mega-event was a dream realised.
"It`s like living a dream. It still hasn`t sunk in and the guys haven`t slept. We have kissed the trophy about a 1000 times," he said.
"I am very proud of the team and myself. Our dream was to make the finals but to win it was extraordinary. Now I understand what it means to be a world champion," he added.