Lawson, who caused a sensation by winning on his debut in the Japanese series in the opening race on Saturday, finished third on the road in Sunday's second encounter behind Tomoki Nojiri and Sho Tsuboi.
However, a five-second penalty for violating the safety car procedure demoted him to fifth in the final classification.
The penalty came about as a result of Lawson trying to create a large enough gap between himself and Mugen team-mate Nojiri, who ran second behind Toshiki Oyu in the early stages, to both make their mandatory pitstops behind the safety car on lap 10 without losing time.
Inging driver Sena Sakaguchi was handed an identical penalty for a similar offence.
However, Lawson feels that at least some of the gap was down to TGM Grand Prix man Oyu intermittently speeding up and slowing down behind the safety car before leading a long train of car into the pits.
"I was disappointed about the penalty," said Lawson, who was running fifth at the time. "The leader [Oyu] was going fast, slow, fast, slow, really aggressively, which is the same as what I did.
"I was conscious of [the gap to the car ahead], but the leader was so erratic, going fast and slow, half the gap was not on purpose for that reason.
"So I don’t understand why I was penalised and not him. But I guess the rules are the rules."
Lawson also expressed his frustration at Super Formula's pitstop window rules, which dictate that a driver cannot complete the mandatory tyre change until the 10th lap.
The caution had been called when Giuliano Alesi got stuck at Turn 1 after being tipped into a spin by Kakunoshin Ota.
"With the way the rules are, if everyone stops behind the safety car, it completely ruins your race if you are the car behind," said Lawson. "It’s quite frustrating, especially with a team as strong as Mugen, with two cars at the front of the field.
"If you’re the second car in line, you’re completely screwed. It’s just the way it is."
Lawson qualified fourth for his second Super Formula race, but failed to make up ground at the start, dealing a blow to his chances of beating poleman Nojiri.
However, the Kiwi driver believes that his race pace was good enough to challenge Nojiri had his race not been so badly compromised by the safety car and subsequent penalty.
"In qualifying, it was my first time with the [knockout] format, so I need to get used to that," Lawson admitted. "In Q1 we had a good balance, but going into Q2 I had a compromised tyre warm-up and I didn’t put a good lap together.
"But the race pace was again really strong, so I think we had every opportunity to fight him [Nojiri]."
Lawson leaves Fuji second in the drivers' standings on 27 points, 14 behind team-mate Nojiri, with the next race taking place in two weeks' time at Suzuka.
