The 28-year-old centre-back started alongside Per Mertesacker in Arsenal's opening game of the season - but picked up two bookings and saw red in a 3-1 defeat to Aston Villa.
He missed the 3-1 win at Fulham but returned against Fenerbahce in the Champions League, only to suffer a kick in the head which briefly saw Bacary Sagna fill in at the centre of Arsenal's defence.
Koscielny was back on the bench for the return leg against Fenerbahce, who were beaten 5-0 on aggregate, but he was back alongside Mertesacker for the north London derby with Spurs and was the rock on which a hard-fought 1-0 victory was built.
The Frenchman admits Arsene Wenger's trust in him helps his confidence - and he feels he has improved his game massively since moving to England.
He told L'Equipe: "Playing a lot of big matches in the Premier League allows you to gain experience.
"I can still make mistakes, but rarely do I play badly for a whole match. After a mistake, you just have to start again.
"My character is calm and serene, so that helps on the pitch. The coach's trust also helps as it allows to liberate yourself and not worry about dropping to the bench if you make a mistake.
"For some months, I've felt better on several levels. In England, you have to be more aggressive in all levels: speed, control, passing, challenges in the air, anticipation... and I've got more physical presence.
"But you will never hear me saying I am unquestionable in the starting XI, either for my club or the national team."
Mertesacker, Koscielny, Carl Jenkinson and Kieran Gibbs have emerged as Wenger's first-choice defensive line-up for this season - and Koscielny admits his communication skills have improved too.
"Am I the real boss of the Arsenal defence?" he said. "I try to talk more. One of my drawbacks is communication, so I am working on that.
"In defence, just one word can solve a problem. This season I feel more at ease at the club, notably considering the language.
"How can I still improve? Maybe scoring more often from free-kicks. But if I always score a £20million goal, that's fine!"
Arsenal pipped Tottenham to fourth spot in the Premier League last season with a 1-0 victory over Newcastle United at St James' Park, where Koscielny volleyed home the winner from six yards out.