Raikkonen, who has not stood on the rostrum since rejoining Ferrari ahead of the 2014 season, had shadowed Vettel over the first half of the Grand Prix after moving up from sixth on the grid to fourth behind the German on the opening lap. He then began closing steadily in the final stages, when he was also able to make use of tyres that were four laps fresher.
By lap 53 he had trimmed the gap to just 1.4s - down from around three seconds five laps prior - only for the safety car to neutralise the race for the final three laps.
"Towards the end of the race I was catching up, I knew I had the speed and I thought I still had good tyres," said Raikkonen, whose last F1 podium came when he finished second for Lotus in Korea in October 2013.
"I could still have had a chance to try and fight for podium but the safety car came in and we know we cannot change that. We got close to the podium - from the next race on we have to have a better weekend, doing everything right in qualifying, and we'll do our best."
Asked whether qualifying or traffic had proved the biggest hindrance to his pursuit of Vettel - Raikkonen instructed Ferrari to ensure lapped cars weren't holding him up several times during the race - the Finn added:" Obviously we were not in an ideal place to start after yesterday's mistake.
"But you know, we did the maximum and as a team I think we got the maximum. Not ideal - obviously we want to be first and second - but that's what it is."