Yamamoto suffered a miserable return season with Nakajima last year after making the switch from Dandelion Racing, with which he won the 2020 title, placing 13th overall with a best finish of sixth.
Despite a poor start to the year, the 2022 campaign turned out to be an improvement as Yamamoto ended a two-year win drought in the wet at Motegi en route to 10th in the standings, only two places behind teammate Toshiki Oyu.
However, in light of Honda stablemate Tomoki Nojiri scoring another title in dominant style this year, Yamamoto says he can't be content unless he is able to beat the Team Mugen driver in 2023.
"Looking just at the results, last year was terrible and we finished the year unable to get a single good result," said Yamamoto. "This year I scored a pole position and won a race, and in the last race I was able to come through from P13 to P6 and score decent points, so it feels like things have improved.
"But there were still some things we haven’t fully grasped, so if I can drive with the same team again next year I want to get better results.
"I’m not driving just to score points or finish on the podium, and seeing what Nojiri has been able to achieve is frustrating. Because I used to be in the position to show that kind of performance, I don’t want to be in a position to have to see that.
"He showed his speed this year and it was natural for him to win the title. However, I am a racing driver and I am determined not to let him beat me, so if I get a chance next year, of course I want to beat him."
Yamamoto notched up his 100th start in Formula Nippon/Super Formula in Sunday's Suzuka finale, with his sixth-place finish marking his best result of the year other than his Motegi victory.
After finishing outside of the points in Saturday in 11th, Yamamoto said he could take some satisfaction away from finishing one place ahead of his younger colleague Oyu in the finale.
"I gained four places on the first lap, two at the start and then two more, so this is the good point of the race," said Yamamoto. "[On Saturday] the pace was so bad and we were struggling with tyre degradation, so we had to make a big [set-up] change for today’s race.
"Finally I had a good feeling and I could score points. The set-up I used is a little bit different compared to Oyu's, so we were able to collect a lot of data and I want to make use of that for next year."
