The spinner starred with bat and ball in the third and final Test against West Indies, taking nine wickets in the match and making a century in his side's first innings.
But his nerves were tested at the end of the final session as India's chase of a victory target of 243 went down to the wire yesterday.
A vital stand of 15 with Ishant Sharma kept India in contention and, needing two from the final two balls bowled by Fidel Edwards, Ashwin blocked one ball and was then run out after hesitating needlessly over the second run needed for victory.
Ashwin told Sky Sports: "In the last few overs, I thought Ishant was playing well and the field was up, so I tried to rotate the strike because I thought we had a better chance of squeezing a boundary through and if we could get a boundary then we were almost there.
"At the end I thought I should take the safer option of defending out one ball and then attacking the last ball, but it didn't work out unfortunately.
"I didn't think it was going to go this far down to the wire. We thought we could prise them out and chase the score down but in the end it was a very good game and a tight game."
The dramatic chase had only been made possible after a West Indian collapse to 134 all out earlier in the day, with India then also losing wickets at regular intervals to put the pressure on their lower order.
Darren Sammy, the West Indies captain, whose side lost the three-match series 2-0, said: "This match was a great advert for Test cricket - we have seen Australia v South Africa and now this match, it was a great end to a Test series.
"We didn't bat well today but at the end we gave ourselves a chance of winning. Well done to the lads, we came to India and fought hard."
"All sorts of things were going through my mind, going down to the end," Sammy said. "At one point, the tied Test came in mind ... The way we batted [590 in the first innings] it would have been heartbreaking to lose the game."
Ashwin bagged 22 wickets in the series against the West Indies while Ojha finished with 20.
India squad for tour of Australia
MS Dhoni (captain & wicketkeeper), Virender Sehwag, Gautam Gambhir, Rahul Dravid, Sachin Tendulkar, VVS Laxman, Virat Kohli, Rohit Sharma, Ajinkya Rahane (batsmen); Wriddhiman Saha (wicketkeeper); Zaheer Khan, Ishant Sharma, Umesh Yadav, Varun Aaron, Praveen Kumar (fast bowlers); Ravichandran Ashwin, Pragyan Ojha (spin bowlers).