The Aston Martin driver was running outside of the points until Mercedes’ Lewis Hamilton retired with two laps remaining, promoting Vettel into 10th to snatch the final point on offer.
Sunday’s grand prix at the Yas Marina Circuit marked four-time world champion Vettel’s final race after a hugely-decorated, 16-year career in the sport.
“I don’t have that much more to say, I feel a bit empty to be honest,” said Vettel, who completed some celebratory doughnuts on the start-finish straight after the race.
“It’s been a big weekend. I can only repeat that the last two years have been very disappointing from a sporting point of view but very, very important and useful for me in my life – a lot of things I realised.
“I think it’s a huge privilege to be in the position we are in and with that comes with a huge responsibility. So I hope to pass on some of the good work. It’s great to see that we have the power to inspire you with what we say.
“There are far bigger and far more important things than racing in circles, but obviously it’s what we love. Through that, if we can transfer some of those important values, I think that’s really big and for that, I think the last two years have been great for me.
“Thank you for the support, thank you for all the messages, and all the love in general. I will miss that. It’s been an absolute joy throughout my career, so thank you.”
Vettel had been running comfortably inside the top 10 until he dropped out of the points-scoring positions due to his strategy.
“I wish it would have been a couple more points,” the German added. “But I enjoyed the race, I think it was a bit of a different warm-up today to get into the race, but once the lights go off it’s full on race mode.
“Today we maybe didn’t go for the best strategy. It was a shame because I think we could have turned the constructors’ championship around for us.
“I had a nice battle with Daniel but I just couldn’t get close enough. But I think it’s nice to have fought the last couple of laps with him, with both of us finishing in the points.
“Overall a big day, and a big thank you to all the support. So many flags and so many smiling faces, which has been very special, very nice. I’m sure I’m going to miss it more than I understand right now.”