Despite that, the New Zealander managed to find fault in his weekend.
"I need to sort these starts because it's two weekends in a row now that I've lost two spots off the line and it's just making our life more difficult," Lawson told Sky Sports television.
"Honestly, it's two slots and around here you can't overtake," added the youngster, who started 10th and one spot ahead of Red Bull's double world champion and championship leader Max Verstappen.
"We did the hard work yesterday and put ourselves in Q3 (the final phase of qualifying) and to lose those spots off the line is a bit tricky".
That said, Lawson was happy with his race and said he gave it everything.
The Kiwi's steady progression, after being given his break when Australian Daniel Ricciardo broke his hand, has made a big impression already.
Thirteenth in the Dutch Grand Prix, he was 11th at the Italian race in Monza and moved up another two places to ninth in Singapore, with his parents on hand to savour the occasion.
The two points made him the 350th driver to score in a Formula One world championship event since the first in 1950.
Japanese teammate Yuki Tsunoda, who retired on the first lap, has scored only three points from 14 races after being unable to start in Italy.
AlphaTauri have yet to confirm their drivers for 2024 and Lawson could team up with Ricciardo or Tsunoda at the Red Bull-owned team if he gets the nod.
"I've been beating the drum since before driving in F1 trying to get this shot and now I have this opportunity I'm just trying to maximise it," said Lawson, who has the seat until Ricciardo recovers.
He is likely to be still in the car for Japan next weekend but beyond that remains uncertain.
"I have this very short window and I basically want to get to the end of it and look back and know that I've done everything I could," he said.
"It's tricky to get a full-time seat in this sport but rather than looking at all those external things for me it's just focusing on every session, trying to maximise each time I'm in the car and show what I can."
