"I'm still really happy", he insisted.
He said: "I thought we would have been able to do better, but yeah we just have to keep working, keep pushing for the next race".
With Hamilton running in second place, Vettel knew he only needed a top-four finish to deny the Brit and quickly started to make his way through the field.
"Not where I wanted to finish, but I really enjoyed the race and getting to be in a battle with these cars with these guys was awesome", he said.
"Ferrari have upped their game here and we go on now to the next race", he acknowledged.
"Once we've done the stop on 11, I knew I would be doing a two-stop", said Hamilton, adding.
Hulkenberg was the "best of the rest" with a solid drive, while team-mate Sainz was just behind him as the French team earned valuable constructor points.
Red Bull's Max Verstappen finished second after starting in 18th place. "I am not sure about the reasoning for the early stop".
"There was definitely a lesson learned for us and we'll definitely go to the drawing board but performance-wise it wasn't our greatest weekend. We made it so hard for ourselves".
"But we've had some incredible weekends this year and still to get a third, I'm still grateful for that - but naturally starting first and finishing third is never a good thing". "Ultimately we wanted to win the race today and I think going backwards two steps is not a good result but as I said, you can't win them all, you can't always get them flawless".
"The way these cars are designed, although they're great on their own we should be able to follow closer than we are and be in a train and be dicing with each other but you don't see that in this series", he told Sky Sports F1. He has not won a grand prix since the Belgian Grand Prix in August and now needs to win the remaining three races and hope title rival Lewis Hamilton scores less than five points in the same period.