Inter coach Roberto Mancini claimed the title hopefuls were unfortunate to lose against the "best team in the league" following Yuto Nagatomo's red card.
Gonzalo Higuain scored a brace as Napoli replaced Inter atop the Serie A table courtesy of 2-1 win on Monday.
Inter were forced to play entire second half with 10 men after Nagatomo was shown a second yellow card for a mistimed challenge on the stroke of half-time in Naples, but the visitors almost salvaged a draw as substitute Stevan Jovetic and Miranda hit the post inside the final 40 seconds.
Speaking to reporters afterwards, Mancini said: "Personally I'm happy because we were always in it, even in the first half.
"Yuto was sent off for a little foul. We would never have lost 11 v 11 and we might even have won it because we played brilliantly. Sadly that's football for you. [Jose] Callejon clearly dived for Nagatomo's first booking, whereas for the second Yuto could have been a bit more careful.
"It was a very open game that was ruined by an unfair sending off, so it's hard to assess. [Pepe] Reina and Higuain were exceptional.
"As I said, that's football but there's no shame in losing if you've played well against the best team in the league and two of their players have had a night like that. On this occasion they got lucky and we didn't."
Inter trailed 2-0 just past the hour-mark after Higuain added to his second-minute opener at Stadio San Paolo.
Adam Ljajic, however, pulled a goal back in the 67th minute.
And despite Inter's numerical disadvantage, they nearly escaped with a share of the spoils in the dying stages as Jovetic hit the crossbar and Miranda's header was tipped onto the woodwork by Napoli goalkeeper Pepe Reina.
"There was a ball we didn't deal with properly at the start and Higuain did superbly to score an amazing goal," Mancini added.
"We deserved more come the end of the match. I thought both Miranda's and Jovetic's headers were going in."