The 33-year-old defender had not played first-team football for the Gunners since he ruptured his Achilles tendon in the 1-0 Europa League semi-final defeat to Atletico Madrid in May, but completed 72 minutes of a straightforward win at Emirates Stadium.
Arsenal boss Unai Emery has favoured a defensive trio of Sokratis Papastathopoulos, Shkodran Mustafi and Rob Holding in Koscielny's absence, but the Frenchman said he was feeling strong after coming through unscathed against Qarabag.
"It has been difficult," Koscielny told BT Sport. "I had difficult moments, it was my first big injury.
"I took a long time away from the pitch and it's difficult but you learn a lot about yourself and the people around you and I'm very happy and calm with myself and more strong.
"For a footballer to miss the pitch is difficult but now it's the end of that and I am smiling.
"I start my season now."
Emery used the Qarabag clash, which came after Arsenal had made sure of their place in the knockout stage, to bring Koscielny and Mesut Ozil back into the first team following their respective injury lay-offs, and he also blooded some of the young players in his squad.
Midfielder Bukayo Saka stood out in an inexperienced Arsenal side, despite having only turned 17 in September, twice going close to becoming the club's youngest goal-scorer in European competition.
He described his full debut as an ambition fulfilled, saying: "I joined the club at the age of eight. I always dreamed of playing at the Emirates.
"I grew into the game, that's what I wanted to do. I should have scored at the end but I don't know what happened.
"On Wednesday in training he [Emery] went through the team and I couldn't believe it. I had to get on with it and focus but I couldn't stop thinking about it.
"My family were buzzing and I couldn't stop smiling last night. They managed to put me to bed early.
"I have to keep playing well at youth and academy level and whenever I get the chance in the first team I have to impress the manager."