Out-of-form opener Sehwag vowed to make a comeback into the national side, saying "I trust my game".
Sehwag paid the price for a prolonged run drought as the selectors trimmed the squad to 14 and decided against picking a replacement for the right-hander, who has scored just 27 runs in his three innings during the ongoing series.
"Will continue to work hard for my place in the team. I trust my game and am confident that, "I'll be back"," he wrote on his twitter page.
He also wished good luck to the Mahendra Singh Dhoni-led side for the remainder of the series, which the hosts are leading 2-0 after crushing victories in the first two Tests in Chennai and Hyderabad.
"Best wishes to the team," Sehwag wrote. Sehwag had failed to fire in five consecutive Tests after getting a hundred in the opening game of the home series against England at Ahmedabad in November-December last year.
He was unable to score even a half-century in two home Tests against New Zealand. During India's last overseas tour, in Australia, Sehwag scored just 198 runs in eight innings.
Indian squad: Mahendra Singh Dhoni (Capt.), Sachin Tendulkar, Murali Vijay, Cheteshwar Pujara, Ajinkya Rahane, Virat Kohli, Ravindra Jadeja, Shikhar Dhawan, Ravichandran Ashwin, Ashok Dinda, Harbhajan Singh, Bhuvneshwar Kumar, Pragyan Ojha and Ishant Sharma.