The visitors were 75/7 when bad light brought curtains down on the match.
In the first innings, Sri Lanka posted 294 in reply's to India's 172.
"Feels good", Kohli said of his 18th Test century, to add to his 32 one-day centuries for India. Declaring at 352-8, India gave Sri Lanka a victory target of 231.
Kohli went on to signal Shastri to send a player with the message.
In hindsight, India could have won the match if they had some more overs to bowl.
Sri Lanka's fast bowlers Suranga Lakmal and Shanaka took three wickets each to rattle the Indian top and middle-order.
The visiting captain said his team needed to learn how to battle in the second innings.
Dhawan, who missed out on a hundred by six runs in the second innings, confirming Bhuvneshwar's wedding asked him about the excitement he is going through.
After staving off defeat by a whisker, Sri Lanka skipper Dinesh Chandimal on Monday said the last 10-15 overs put his side under lot of pressure on day five of the first Test against India at the Eden Gardens here.
"Dhawan is available for selection for the third test".
"The duo made a request to the selectors and the team management to release them owing to personal reasons", it added, without elaborating further.
Bhuvneshwar, who took eight wickets in the match, is scheduled to be married to his fiancé Nupur Nagar on November 23.
The second match in the three-test series will be played in Nagpur from Friday.
"India Test squad for the second Test: Virat Kohli (Captain), KL Rahul, M Vijay, Cheteshwar Pujara, Ajinkya Rahane (Vice-Captain), Rohit Sharma, Wriddhiman Saha (wicket-keeper), R Ashwin, Ravindra Jadeja, Kuldeep Yadav, Mohammed Shami, Umesh Yadav, Ishant Sharma, Vijay Shankar", the statement added.