Vettel inherited the race lead from pole sitter Lewis Hamilton after the Briton retired with a gearbox failure and the German held off the other McLaren of Jenson Button and Alonso's Ferrari to reignite his hopes of a third straight title.
Alonso has made a habit of converting poor qualifying positions into big points this season to forge ahead of the field and the double world champion was able to draw on his experience to achieve another strong result in Singapore.
"It was the best I could hope for as we were not very competitive this weekend in terms of pace," Alonso told reporters after recording his 81st podium in Formula One, putting him third on the all-time list in that category.
"But we qualified well, which was the best part of the weekend. If you are stuck at the rear of the race then you have a lot of problems," he added.
"It was a very positive weekend. We only lost points to one of our major contenders which is good considering we are not quick enough."
Looking ahead to the Japanese Grand Prix in Suzuka on October 7, Alonso is hoping for an improved performance in qualifying to stay ahead of his rivals with just six rounds remaining in the 20-race season.
"It's a little bit difficult to predict as it has been a year of ups and downs for all the teams. Here we (Ferrari) could only qualify fifth and 13th which is not what we are hoping for," he said.
"We need to do better at Suzuka, it is similar to Silverstone where we did well, so we're hoping for an improved performance."