Koscielny completed the scoring in a rousing 2-0 win with his first goal since suffering a ruptured Achilles tendon last May.
But the truly impressive element of a victory that brought the Gunners to within three points of their opponents in the final Champions League qualification spot was tireless collective effort – something the former France defender welcomed seven days on from a lacklustre defeat at West Ham
"Today we needed to win. We did a mistake last week and it was a game of six points," Koscielny told BT Sport.
"If we lose, it would be nine points; if we win just three points. We are still in the race for the top four.
"It was important, the commitment was amazing from all the boys. We talked a lot and we showed on the pitch which way we want to go together.
"It is good to play like this. We want to fight for each other.
"When we talk about a clean sheets it is not just about the defenders. We showed everyone working together; the strikers work and help the rest of the team. Then at the back it is easier to win the challenges.
"It is good for our head – we can keep this [mentality] for the rest of the season."
Alexandre Lacazette scored a superb 14th-minute opener for Arsenal, deftly engineering space in the box to beat Kepa Arrizabalaga at his near post.
"This is what the coach asked us to do in the dressing room – [press] from in front. We worked, we fought all the game," he told BT Sport.
"We are now three points to Chelsea so we are still in the race and we will fight until the end."
Koscielny's goal – an attempted header than spun in off his shoulder – was not so easy on the eye but every bit as valuable.
"I did my work in the gym," he joked.
"We know a free-kick or a corner is always important in modern football, the small details. I'm happy to score."