India defeated the hosts by an innings and 92 runs in the first Test, which also happens to be the first assignment of new head coach Anil Kumble.
Tendulkar congratulated Kohli, Kumble and off-spinner Ravichandran Ashwin, who notched up a seven-wicket haul to set up India's biggest margin of victory outside the sub-continent.
"Congrats to @imVkohli led #TeamIndia on a wonderful win. Great performance @ashwinravi99 & wonderful debut for @anilkumble1074. Keep it up!" Tendulkar wrote on his twitter handle.
All-rounder Irfan Pathan also heaped praise on Ashwin.
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"Scoring 100 n taking 5-for in the same game is so special, enjoy every bit of it mate. Very well done @ashwinravi99," Irfan wrote on Twitter.
The second Test begins in Kingston on July 30.
Former India spinner Bishan Bedi also praised India and asked them to continue their good run in the series.
"Indns've set terrific trend n Antigua..& now 2 tighten screws only 4-0'll do..& all by Innings' win wud b icing on the cake!Gr8 job India!!!," he tweeted.