India virtually bowed out of the tournament after suffering a 69-run defeat against Sri Lanka in their last game here on Friday, leaving millions of their fans back home in a state of shock and despair.
Their surprise five-wicket defeat against Bangladesh in the first game has already sparked unrest in some parts of the country.
"You've got to be concerned in light of the recent incidents, but I am quite confident the systems are in place to look after the security of the team and individuals involved," he said.
"When India wakes up 'morrow, there will be a lot of disappointment and anger, but they should realise it's just a game."
Chappell said he was willing to own up some responsibility for his team's failed campaign, which saw India put in their worst performance since the 1979 edition in England.
India were the champions in 1983, semi-finalists in 1987 and 1996, and runners-up to Australia in the 2003 edition in South Africa.
"I've to take some responsibility as a coach. Nothing's wrong with the support coaching staff and the players who worked very hard," he said.
Chappell also admitted his team failed to live up to expectations after having prepared well for the tournament.
"We came here with huge expectations, but didn't live up to them. The dressing-room is a quiet place at the moment," said the former Australian Test batsman who took over as India coach in 2005.
"The team was under pressure and I think the pressure had a bearing on what happened today. The pressure built up after the Bangladesh game.
"Our bowlers did well today, but we did not have any good partnerships. We could not perform when the time came."
India were bowled out for 185 chasing a 255-run target on a good batting wicket at the Queen's Park Oval, with skipper Rahul Dravid (60) and Virender Sehwag (48) alone defying the Sri Lankan attack.
When asked what India were taking away from the World Cup, Chappell said: "A lot of disappointment. It's one of the most disappointing days in Indian cricket.
"There's a cause for serious introspection, but I believe it should not start today."
India skipper Rahul Dravid said he hoped the players would not be harmed when they returned home.
"I'm not really worried about security and I hope the players wouldn't be under any physical danger. To be honest, I don't expect that to be the case. I am sure people will be disappointed," he said.
"They have invested a lot of hope in this team and we haven't delivered. So, they are entitled to be disappointed. But I just hope that no-one in is in any physical danger."
Dravid said it was hugely disappointing he and senior team mates such as Sachin Tendulkar, Saurav Ganguly and Anil Kumble might end their careers without a World Cup medal.
"It is not an ideal scenario," he said. "If you were writing a fairytale, you wouldn't write it this way."
"That is the beauty and cruelty of sports sometimes."