Vettel ran third for most of the race but benefitted from Max Verstappen receiving a five-second penalty for an unsafe release. At one point it looked like the German was in the prime position for the victory but it never materialised but he did end Mercedes' one-two streak.
Lewis Hamilton struggled with his tyres for most of the race but survived and Vettel admitted it wasn't easy managing the tyres.
"A tough race to manage, at Monaco something always happens, Max must have had an incredible stop, I saw them (Verstappen and Bottas) touching in the pit lane," Vettel said after the race.
"I thought there was a good chance we could capitalise on Valtteri's puncture, which was a shame for him, and we tried to stay in range (of Verstappen). I wanted to put some more pressure on, I just struggled with my tyres, not as badly as Lewis and Max's, but mine were just not getting hot.
"It was a bit tricky but a great result and we have a lot of work to do - we are not quick enough compared to these guys. Niki (Lauda) would be happy today, he will always be around, we will definitely miss him. He's an icon in the past and in the future, my thoughts are with his family."