The opening pair of Jasprit Bumrah and Bhuvneshwar Kumar shared six wickets between them as India strolled comfortably to victory by 36 runs and inflict Australia's first defeat of the tournament.
"It's a dream to have a bowler like him (Bumrah). He's one of the best in the world both at the beginning of an innings at the death," 56-year-old Arun said.
"My job is just to remind him and Bhuvi (Bhuvneshwar) about their plans and what they've done well in the past," he added.
Arun insisted that in a long tournament, every bowler has to be ready. He said: "It was always our plan to open the bowling with Bumrah and Bhuvi because he moves the ball around in English conditions and he bowls well at the death."
The pitch at The Oval had been used four days previously for New Zealand's win over Bangladesh, which influenced India's tactics when they came to defend their sizeable total of 352.
As Australia struggled to stamp any authority on their run chase, Arun said: "We had planned not to give the batsmen any width and also to take the pace off the ball and I thought we executed the plans very well."
He added: "It was a conscious plan to bowl short to David Warner - and you saw that most of the short balls we bowled at him he wasn't very comfortable with."
Arun admitted that conditions have been different from some of the pre-tournament hype about huge totals and matches simply being run-fests.
"In England, the ball moves around. You saw that when England played against Bangladesh they were nine off five overs but ended up with 60 in the powerplay. If you can assess the conditions and then you can launch later," he said.
India scored only 41 runs from the first ten overs but amassed 116 of the last ten to set a target of 353 that proved to be beyond Australia's reach in the end.
Arun also backed spinner Kuldeep Yadav, 24, who blew England away at Trent Bridge with 6 of 25 last year, to return to form after a difficult IPL tournament this year.
"Every bowler goes through a stage where they get hit. It's my job to remind him about all the good things he has done in the past and build his confidence," he said.
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