Wright, the coach of ICC World XI team playing in Australia in the Super Series, left as India's coach last April under pressure stemming from four consecutive One-day defeats to fierce rivals Pakistan.
Former Australian Test captain Chappell was made his successor and has since been embroiled in a row over his desire to get rid of Sourav Ganguly as team captain.
India's cricket chiefs have worked out a truce between the warring duo and have asked them to mend their differences for the sake of the national team.
Wright, whose five years as coach included Test series victories against Australia and Pakistan, admitted to poor results in the last months of his tenure and said he hoped that straight-shooting Chappell would fix it.
"My last seven months with the (India) One-day team, the form was poor and Greg's going about sorting that out," Wright told reporters here Saturday ahead of the final Super Series One-dayer with Australia on Sunday.
"There will always be a couple of bumpy issues along the way when you are in a coaching situation, but I hope my successor Greg and his team can take it a bit further forward."
Wright defended his gentlemanly demeanour against criticism that he was not tough enough to get his way in the politically-charged world of Indian cricket.
"I don't want to get into that conjecture, but the bottom line from my perspective as a coach is I work in my way. I know that several people made judgments on how I approached the job and generally it's from their perspective," he said.
"I know the way I did the job and I feel we made progress. I don't have anything to add. At the end of the day you do it the way you want to do it. I certainly don't have qualms about not being hard in the job.
"I think you have to ask the players about those sorts of things. I had several years with the team, I enjoyed it, I loved the fans over there. It was probably my most enriching cricketing experience.
"We took the process of trying to get a team that would keep everyone ... happy and take it a stage forward and I hope my successor Greg and his team take it a bit further forward."
Wright said he was a keen observer of Indian cricket and had no doubts that India could one day reign as the world's number one cricket team.
"I know that they can play and they'll get the results," he said.
"I always felt that India could be number one. They've ranked third in the Test rankings and One-day form can turn around very quickly, as we showed in the (2003) World Cup and the (2004) ICC Championship."
India have a seven-match One-day series against Sri Lanka starting on October 25.