India were beaten by 298 runs in the final Test, in Adelaide, losing the series 4-0.
India's opener chose to remind fans of the past successes – most recent being the 50-over World Cup win last year.
"When we won the World Cup everyone was happy and cheering for Team India, and now the time we need the support of the fans and everybody, they should back their own team," he said.
Sehwag, 33, who averaged 24.75 runs over the series, said accusations the India team did not care enough about losing a Test series were well wide of the mark.
"It's very unfair," he said. "I think everybody cares about their performances, about India losing the game. We are very passionate about our game and passionate about our team and it's a shame that people are talking about that.
"If you lose the game you should work it out what went wrong and come back and perform well in our next games. We are trying that, but it's not happening and it doesn't mean we are happy to lose here.
"If you look at the Australian team, they were struggling as well in the Ashes last year and they got out for 47 in South Africa, so it happens with every team so we have to rebuild the team," he said.
Sehwag also disagreed that the team needed to drop their ageing players, such as Sachin Tendulkar, Rahul Dravid and VVS Laxman.
"I don't think [changes] are due because the same team played in the last couple of years when we became the No 1 team in the world with the same batting and bowling line-up," he said.