Real Madrid won 5-0, with Kylian Mbappe hitting a hat-trick, along with Eduardo Camavinga and Brahim Diaz also scoring.
Afterwards, Xabi said: “We came here with the clear objective of winning the match. It's the Champions League and we wanted to make a good start. We've got six out of six and the next objective is Juve at home.
"We scored five goals, achieved our objective and played well. The players have been committed and doing things well. We'll think about Villarreal now.
“Mbappé is in a moment where he is decisive in every match. He's effective and clinical in front of goal. We have to harness his talent. He scored a spectacular goal in the derby and we need him to flourish. I'm delighted with his goals and also with the positive influence he has on his teammates. He's putting in the work and he can have a spectacular season.”
Kairat made it uncomfortable
On the way Kairat attacked them at the start, Xabi said: “We were a bit uncomfortable. They pressed us hard, but when we linked up with Arda, we found the players up front and there were good chances to break their pressure. We were a bit caught off guard at first.
“They deserve to be in the Champions League. We had a fantastic reception and I wish them all the best. We came here to do what we came here to do, but from now on I wish them the best of luck.”
Xabi, meanwhile, said of Arda Guler: “He's been playing as an attacking midfielder to make the most of his quality. He's been playing in a central position behind the striker to link up with Mbappé. He scores goals and has the quality to deliver the final pass. Today, he's also been turning very well in midfield.”
Asked about Vini Jr's reaction to his substitution, the coach added: “You always have to manage anger and control it. Nothing has happened so far. Vini Jr. hasn't complained. It was a comment that was unrelated to the matter at hand.”