Arsenal, who had won all eight matches in the league phase of the competition, looked set for defeat at the BayArena before substitute Kai Havertz converted an 89th-minute penalty against his former club.
Arteta admitted the Gunners were not at their best despite securing an important away result.
"I liked that emotionally we understood what we had to do, but the level of execution obviously has to be better," said Arteta.
"And it will be better in the second leg. We'll adapt a few things and move on."
Arsenal had started brightly and almost took the lead when Gabriel Martinelli crashed a powerful effort against the crossbar during the first half.
However, Leverkusen struck moments after the restart. A dangerous header from Martin Terrier forced a brilliant save from goalkeeper David Raya, but from the resulting corner Robert Andrich slipped away from Eberechi Eze at the far post to head the hosts in front.
The goal was ironic for Arsenal, who have built a strong reputation for scoring from set-pieces this season.
"There's always two sides to that," Arteta said. "One is the opponent picking up on that lack of attention or urgency. The other one is us because we knew about it and we weren't ready for that situation."
Arsenal's equaliser arrived late in the game when substitute Noni Madueke drove into the penalty area and was brought down by Malik Tillman. After a VAR review confirmed the contact, Havertz calmly sent the goalkeeper the wrong way from the spot to level the tie.
"Football is a funny game and it brings special stories," Arteta said with a smile. "For him to come back here after such a long time and score such an important goal is a big moment."
Leverkusen coach Kasper Hjulmand disagreed with the decision.
"Disappointed with the penalty at the end. I don't see a penalty there but that's the way it went," he said. "For me, it just wasn't."
The tie now moves to London, where the second leg will be played at Emirates Stadium on Tuesday, 17 March 2026, with a place in the quarter-finals still very much in the balance.