Alonso has seen a 44-point lead he held over Vettel following his win in Germany in July eroded on the back of the latter's stunning late resurgence in his Red Bull.
Four consecutive victories recently allowed Vettel to overhaul a man he is going head to head with in their fight to become a three-time champion, opening up a 13-point cushion.
In Abu Dhabi last time out, when Vettel was dumped to the back of the grid as punishment for a fuel irregularity after qualifying, Ferrari star Alonso would reasonably have expected to have made significant inroads.
But Vettel produced a stunning drive to finish third behind Alonso who only managed to claw back three points going into Sunday's United States Grand Prix to leave the gap at 10.
Vettel is overwhelming favourite to win his third successive crown, and if he can finish 15 points ahead of Alonso at the Circuit of The Americas, he will complete the three-peat.
Alonso, however, is undeterred as he simply attempts to push Vettel to the wire in Brazil next weekend, as was the case in three of his previous bids for the championship.
Asked for his emotion now compared to the scraps in 2006, 2007 and 2010, Alonso said: "I'm much more relaxed, much more focused.
"In 2006, in fighting with Michael (Schumacher) in the last race in Brazil, it was quite a stressful, intense weekend. It was not easy to focus, sleep, or things like that because it was emotional.
"The year after, in 2007, it was also a very stressful last race in fighting Lewis (Hamilton) and Kimi (Raikkonen).
"In 2010, we arrived in Abu Dhabi and I was more calm, more confident and things were very good for us in terms of preparation, approach.
"But the race (losing out to Vettel) was what it was. We did not win at the end.
"Now, for these last two races, I feel normal.
"This is the fourth time I'm fighting for the world championship, with the hope it will go to the last race.
"You can feel the difference of being focused, concentrated on doing the job, understanding if you do everything perfect you have a chance, or if you make a mistake, you lose the chance."
The COTA track is new to all and would appear to represent a level playing field this weekend, with Alonso not seeing any advantage.
"We will all adapt very quickly to the track in the first practice," said Alonso.
"We've also all been preparing for the race in simulators, which is the same as any other race."
Alonso's confidence, however, remains undimmed despite the situation as he said: "I'm very confident - I trust the team and myself.
"We are honest with ourselves, we know we don't have the quickest package, with our qualifying average being sixth or seventh (on the grid).
"If we're sixth or seventh here on Saturday then people will think we're saying bye bye to the title.
"But our strong point is scoring more than others on a Sunday, and I'm sure we will do this in the next two races."