Richards, widely regarded as the most destructive batsman in history, said a lack of self-belief had sent India crashing to their worst World Cup performance since the 1979 edition in England.
India -- the 1983 champions and 2003 runners-up -- were stunned by Bangladesh in their opening match before suffering a second defeat against Sri Lanka to be knocked out of the tournament.
"Like many of their fans, I find India's ouster from the tournament as mind-boggling," Richards, 55, wrote in a syndicated column that appeared in Indian newspapers.
"I would not blame the team management for this debacle, but there has to be some reason why a team as supremely talented as India does not achieve more success.
"The reasons have less to do with talent and potential and more to do with mental strength. Each player, especially the experienced one, is responsible for himself and capable of self-training and managing his mental preparation.
"These are aspects that come from within, so blaming coach Greg Chappell or even captain Rahul Dravid is not going to take Indian cricket ahead.
"I would certainly like to help India in this aspect of their preparation if asked to.
"I have always enjoyed a challenge as a player, and would enjoy the challenge of instilling self-belief and confidence in a group of players as talented and promising as the Indians."
Richards, who helped the West Indies win the first two World Cups in 1975 and 1979, said the Indians would do well to learn lesson from his team's experiences.
"I remember we were devastated when we lost the 1983 World Cup final (to India)," he wrote.
"That is why we came in full force and with great intent to win when we toured India later that year. We needed to prove to the world and more importantly to ourselves, that we were the best team."
That year, Clive Lloyd's men avenged the World Cup defeat with a 3-0 victory in the six-Test series and blanked the hosts 5-0 in the one-dayers.
Richards said he hoped India would bounce back on the tour of Bangladesh in May for two Tests and three one-dayers.
"They should regroup and convince everyone that what happened in Port-of-Spain was a blip, and nine times out of 10 there can be only one winner in an India-Bangladesh encounter," he wrote.
"Having said that, we must also acknowledge that the Bangladeshis are a talented, fast-improving bunch. They remind me of the Sri Lankans in the late 1980s, and therefore cannot be considered pushovers."
India's cricket chiefs, who are due to discuss the World Cup debacle in Mumbai on April 6 and 7, declined to commit themselves with respect to Richards' offer of assistance.
"We will decide on the future course of action in Mumbai," said Indian cricket board secretary Niranjan Shah.
The brain-storming session is to include first-hand accounts from Chappell and Dravid as well as a discussion with former captains like Sunil Gavaskar and Kapil Dev.
Richards, who retired in 1992 after being overlooked for the World Cup that year, scored 8,540 runs in 121 Tests at an average of 50.23 with 24 centuries.
He also made 6,721 runs in 187 one-dayers at 47.00 with 11 hundreds.