Ashwin picked up 12 wickets at an average of 48.66 in the four-match series but insisted that it was a decent effort as the wickets Down Under are not particularly conducive for spinners.
"To say it (performance overseas) will get better by the time I'm done, is not how I look at this game. I think I came of age when I played in Australia this time. More than anything else, I think I created a lot of wicket-taking opportunities and put a lot of pressure on the batsman," Ashwin told 'ESPNCricinfo'.
Ashwin has been fairly consistent on sub-continental assignments, grabbing 100 wickets from 16 Tests at an average of 23.87. However, he has 24 wickets in 9 Tests abroad at an average of 56.58.
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"If I play a Test in India, I might end up picking five wickets immediately but it might happen in the third or fourth Test in England or South Africa. It hasn't happened but might happen soon," he asserted.
Ashwin said he wants to be an important factor in the team's performances outside the sub-continent.
"Maybe that is what was needed for me to become a better bowler. I firmly believe that was fate because until then I had played 18 Test matches without a lot of bad games.
Talking about the team's new Test captain Virat Kohli, Ashwin said they are starkly different personalities but get along just fine.
"Whichever team I've turned up for, I've always wanted to contribute and be the prime performer. To a degree, Virat is very similar and I love that character of his because we both go about our business in a very different manner," he said.