England, set an unlikely victory target of 500, survived India's charge and closed on 369 for six. Pietersen scored 101 for his 10th Test century to frustrate the Indians, who still won the series 1-0.
Kumble reacted angrily when he attempted to field off his own bowling and collided with non-striker Pietersen, who he thought was trying to obstruct him. Kumble then had a heated verbal exchange with the England batsman.
"He's a fierce competitor," Pietersen told reporters. "India were trying as hard as they could to win and he was fighting for his country. I was ball watching and got in his way."
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"It was nothing serious, (but) Anil can get quite worked up on the field when he's bowling and trying very hard," Dravid said.
"He was in his 30th over and was trying to win a Test match for India. There's no prouder man than Kumble when he steps on the field to represent India. He gives it his all and when he gives it his all it can get the better of him.
"It shows the effort he has put in this series and over his career. Anil has been a top man and I'm really happy for the way he got a hundred - it was one of the most popular hundreds that I've seen," he said, referring to Kumble's 110 not out on Friday that was India's only century in the series.