Arthur was seen sharing heated words with Shanaka after Sri Lanka's series-conceding loss in second ODI.
The animated exchange was caught on camera soon after the home team’s series-conceding three-wicket defeat and Shanaka feels it is something Arthur shouldn’t have done publicly.
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"This is something that should have happened in the dressing room," Shanaka told reporters on the eve of the third ODI. "He (Arthur) wanted to know if I deviated from the agreed plan and I said no."
The Lankan captain further said the coach questioned if he had changed tactics they had agreed before the match.
"There was no heated exchange. I explained what happened. I said I did not change plans and there was no deviation."
Chasing 276 to win, Team India were reeling at 193/7 before Deepak Chahar (69 not out off 82 balls) and Bhuvneshwar (19) shared an unbeaten 84-run stand to take the visitors over the line with five balls to spare.
After the game, Arthur was seen sharing heated words with Shanaka. He appeared to indicate that Shanaka should go with him off the field but the captain did not budge while Arthur walked away, in a video that is doing rounds on social media.
Arthur called it a "good debate" when he received flak for his behaviour on social media.
"It was actually a very good debate, no need to make mischief out of it," Arthur said on Twitter while responding to former Sri Lanka cricketer Russel Arnold's comment that the exchange should have taken place in the dressing room.
The third and final ODI of the series is due to be played in Colombo on Friday (July 23).
(With AFP inputs)