The former New Zealand captain ended his 4-1/2 year tenure in disappointment after Pakistan swept to a 4-2 one-day series victory with a huge 159-run win in the sixth and final game.
"We tend to play the big tournaments pretty well and this is a hard, bitter pill to take," Wright said in a farewell news conference after the match.
Wright, who took over as India's first foreign coach in November 2000, regarded defeat to champions Australia in the 2003 World Cup final as one of his biggest disappointments.
"I have had my disappointments," he said. "You get so far and you can't nail it."
India have struggled in limited overs cricket since the final and Wright urged the players to learn from such defeats so they could become a major contender for the 2007 tournament.
"We can be very brilliant and sometimes be at the other end of the scale, probably a little bit (like) today," he said. "We need to find that middle ground consistently."
Wright, credited with improving Test performances and player fitness, said the team should realise they owe more to the passionate fans in cricket-mad India.
"I have always felt the passion of the Indian fan is very, very special and very valuable," he said.
"Cricket in their life plays a big part and I have always felt they deserve a good team, particularly a good fighting team."
Wright said he did face frustration in some areas during his tenure and felt a twinge of regret that the India coach was not a selector on tour.
"You have to accept when you come into a position there are constraints and frustrations and you have to work with the system," he added.
He said he was still undecided on his future but did not rule out coaching another team soon.
