Kumble, the world's third-highest wicket-taker in Tests with 619 scalps behind Sri Lankan Muttiah Muralitharan (800) and Shane Warne (708), said India had the ability to strike back.
"The desperation and hunger which has been the hallmark of this team was missing in the last two Tests. They will have to get that hunger back. If that comes in, the rest of it falls in place because the ability is there," he wrote.
"The way we lost hurt more than the loss itself. These are the same players who have taken Indian cricket to such great heights, and they realise what the issues are."
India lost the first Test by 196 runs and the second by 319 runs.
Former India captain Sunil Gavaskar also said Sehwag's return would be a big boost for Mahendra Singh Dhoni's team.
"Sehwag joins the team and even if he fails in the two-day warm-up game (starting at Northampton on Friday) he must play in the next Test," Gavaskar wrote in the same paper.
"He can lift this team up and can just be the tonic this team needs. Yes, India are two down but a hurricane start from the Delhi dasher (Sehwag) can help turn it around."
Sehwag, known for dominating bowling with his brilliant strokeplay, has scored 7,694 runs in 87 Tests with 22 centuries.