"We couldn't match some of what they were willing to do and sign and (Indonesia) really wanted him to be there so more power to them," he told racer.com in a story that was subsequently withdrawn from the website and replaced by a different version.
Haryanto, who is backed primarily by Indonesian state oil and gas company Pertamina, was confirmed by the team on Thursday.
The company's chief executive told reporters in Jakarta that Pertamina had contributed five million euros (£3.8 million) towards securing the seat.
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Rossi told Reuters that, while he had felt 'kind of helpless' in the face of Indonesia's support for Haryanto, some of his other comments to Racer had been misconstrued.
"At the end of 2015 I felt I was in a very strong position to be in one of the race seats in 2016 but obviously being a very attractive team with the Mercedes power, it was always going to be a challenge," he said.
"I feel we did a very good job from our end to try to make it happen. But unfortunately the way the sport sometimes works, all the cards don't fall in your favour."
Rossi said he was still in "very positive discussions" with Manor about the future and hoped to return to Formula One "as soon as possible."
The team, who competed as Marussia last year and have the smallest budget in the sport, have always been open about their need for drivers to bring financial backing to secure the seat.
They went into administration at the end of the 2014 season before emerging under new ownership, and money remains tight.
Their other driver is Mercedes reserve Pascal Wehrlein, with the German manufacturer and reigning champions also providing the team's engines.
"We are trying to keep my hat in the ring in Formula One and keep the relationships alive," said Rossi.
"The relationship I have with Manor is very strong but...it's no secret I have to look at other disciplines and see what other opportunities exist out there."
(The story was refiled with driver clarification)
(Reporting by Alan Baldwin, editing by Toby Davis)
