Marco Asensio scored the only goal four minutes before half-time, but Los Blancos' performance levels dropped after their midweek Champions League win against Roma.
"They are three important points from a complex and difficult match," Lopetegui was quoted in Marca.
"We lacked energy in the second half and lost control. There was fatigue because we played two demanding games in three days."
Real spurned numerous other chances but struggled for fluency against dogged opponents, who struck the frame of the goal through Borja Iglesias in the second half.
"Espanyol played well and were organised, and we knew it would be difficult," said Lopetegui, who remains unbeaten in LaLiga since replacing Zinedine Zidane in the summer. "We made the Asensio goal profitable."
The former Porto and Spain head coach rested Gareth Bale, Dani Carvajal, Marcelo and Toni Kroos, with Alvaro Odriozola, Nacho and Dani Ceballos starting, while Thibaut Courtois replaced Keylor Navas in goal.
"The emergence of new players is positive, they have all played a full game, though Nacho's (yellow) card has affected him a lot," said Lopetegui.
Real's £37.2million Brazilian summer signing Vinicius Junior was left out of the squad.
"We had to assess how everyone was doing and finally Valverde came in (instead of Vinicius)," Lopetegui added. "We'll see if he plays with (the second team) Castilla on Sunday."
Espanyol coach Rubi said he was pleased with his side's display, but was disappointed they left the Bernabeu without a point.
"It has merit to have caused Real Madrid problems. We bothered them and I think we have done a good job," Rubi said.
"We made it difficult for them to find spaces. It is very difficult to come here and make Real Madrid look uneasy.
"We have done a good job closing spaces, although in the first half they made us run a lot because we could not get the ball as much as we wanted."