Chigumbura scored his second One-day hundred but the hosts fell short by just four runs, chasing 256 to win.
"I was looking to stay calm but inside I was nervous. The way Elton Chigumbura batted, it could have gone either way. Credit to both batsmen and bowlers," Rahane, leading a second -string team, said after the match.
"I am happy, all guys played well today. (Ambati) Rayudu batted really well because the wicket was not easy early on. The way he batted it was brilliant to see from the dressing room. It was a crucial stand between him and (Stuart) Binny," he said.
"We knew our fielding was good. So it was additional 10- 15 runs added to the score in a way. Credit goes to Bhajji pa (Harbhajan Singh) and Axar (Patel), they bowled well and later Dhawal Kulkarni and Bhuvneshwar Kumar bowled well under pressure,"
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He said.
Heartbroken after his unbeaten 104 went in vain, Zimbabwe captain Chigumbura said he was disappointed but hoped to learn from mistake and come good in the next match.
"It was disappointing to lose the game after getting so close. It is something we can learn. I thought it was a good wicket to bat on, but we kept losing wickets," he said.
Ambati Rayudu, who was adjudged Man of the Match for his career-best knock of 124, expressed happiness that he could help his team win the match.
"It was very tough to bat in the morning. Me and Ajju (Ajinkya Rahane) were batting well until he got out. I am happy that I took the responsibility today. Contributing to the team is more important, we won today so I am happy," said the 29-year-old.
"I was constantly telling Binny to hold back a bit till the 42nd over as he couldn't afford to lose wickets then. He was batting well and I am happy he came good in the end," he said.