The Champions League winners had goalkeeper Thibaut Courtois to thank for keeping the clean sheet when he was sharp enough to deny Antoine Griezmann and Diego Costa in one on one situations.
Casemiro also appeared to handle the ball in the penalty box, but Atletico were denied a penalty. However, Lopetegui insisted that they were the better team on the night.
"We were the better team by far, but if you don't score a goal, then, obviously, you can't win," he told reporters, according to Goal.
"The goals will come, I don't have any doubts about that. We created a lot of chances, and if we keep doing that then I've no doubt the goals will flow.
"Atletico are a great team. They have joined the elite with some magnificent signings, they've a spectacular squad.
"They are contenders to win everything, so I'm happy because we were better than a great team."
Real also suffered a setback after Gareth Bale was subbed off due to an injury, but Dani Ceballos injected some much needed incision into the attack.
"Gareth felt something in his adductor in the first half," Lopetegui added. "He came off as a precaution and will have tests tomorrow, so we will see what he actually has.
"Dani came on today and did fantastic. He played very well when the team was more balanced and playing better in the second half.
"That meant we won the ball back a lot in their half. Dani showed the personality and character he has, his physical and technical gifts."