Kasparov, during Anand's world championship match against Boris Gelfand, had said that the Indian lacked motivation and was "sliding downhill" these years.
However, Anand succesfully defended his crown, which was a befitting answer to his critics such as Kasparov.
"We were asked about his remarks. He is the man who regrets leaving chess. He misses the attention he got in chess, somehow wants to be there. May be he should play again," Anand said at his first press conference in the country after winning his fifth world title.
Anand said maybe Kasparov wants him to retire.
"Kasparov retired in 2005, he has been trying to make me retire since 2011. You just have to develop a thick skin as a public figure," he said.
When Anand had drawn the sixth straight game against Gelfand during the world championship in Moscow, Kasparov hit out at the Indian, saying: "What I think with Vishy is that he has lost motivation. Gelfand hasn't won a single game against Vishy since 1993.
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"As for Vishy, I think he's sliding downhill these (last) years. He wants to win, he knows he's a better player, but it's not enough."
The Indian chess legend said he shuts himself down when he is locked in a tournament, to avoid distraction.
"In general I try not to read anything during world championships. I try to stay in a bubble. The idea is to block it out. He came to the match venue and gave a PC," he said.