The Australian topped the timesheets during qualifying for the Singapore GP on Saturday but had to settle for third eventually, behind Hamilton and Rosberg.
Hamilton, who is 22 points behind Rosberg in the race for the world title, claimed his sixth pole of the season, and was 0.173 seconds quicker than Ricciardo.
The 25-year-old Ricciardo, who has won two of his past three races, is 72 points adrift of Rosberg, but is optimistic about his chance of closing the gap at the Marina Bay Street Circuit.
"It's definitely encouraging," said Ricciardo.
"Coming into the weekend I thought if we could be within two or three tenths it should give us a bit more [of an] optimistic chance in the race to stay with them.
"So I think we ended up a bit closer than we thought we would, particularly after yesterday.
"I think it was a good day."