Gabi Martinelli and Bukayo Saka struck as Arsenal won their Champions League tie 2-0.
"I'm really happy," said Zubimendi afterwards. "At the end it was the first match in the Champions League at home - the atmosphere was amazing. We scored two and kept a clean sheet.
"It was really demanding. We started really well but at the end they pushed a lot in the second half. I think we suffered in some moments where we shouldn't have."
The Spain midfielder added: "The adaptation has been good, but I think I can do it better. It's true that the team is amazing, the staff gave me a lot of confidence. The feeling on the pitch is good, but I think I have more to do in this club.
"We want to keep the momentum and win as many games as possible. We will recover well and prepare for the next game against West Ham."