"This victory is sweet. It is special to come and beat Pakistan on their own soil. It is very satisfying," said Kumble, who took 15 wickets in the three-match series to emerge the most successful bowler on the tour.
Kumble, who missed the five-match One-day series due to a shoulder injury but recovered in time to play in the Test matches, said the win highlighted the never-say-die attitude of the Indian players.
"There is a lot of talent in the team and the youngsters have made a lot of progress. I think one of the main reasons for our success is we don't give up easily and keep fighting till the very end."
Expressing satisfaction at his own performance, Kumble said, "I had a great time in Australia (24 wickets) and here in Pakistan. It is great to play a part in overseas victories. That has always been my ambition."
The veteran, with 397 wickets from 84 Tests, needs three more wickets to become only the second Indian to take 400 or more Test scalps.
"400 would be a big achievement but what is more important is that I help the team win matches. I would like to keep bowling this way."