Real Madrid raced into a two-goal lead before Abiel Osorio headed Elche back into the contest and Fer Niño levelled, only for Espí to restore the visitors' advantage late on. Mourinho conceded his side had made the contest far harder than it needed to be.
"Just three points. Obviously after the first half the feeling was that it should have been three, four or five goals by the second half. We dropped the intensity, left a lot of space," Mourinho said.
"I tried to add more consistency in midfield with Jude and Brahim, but they got their second goal right then, and on grounds like this, with this atmosphere, a team that looks dead comes back to life."
The Real Madrid boss pointed to a recurring pattern of his side failing to kill off matches once in control.
"My only criticism is that we can kill games off and we don't do it, and we've given life to a team that looked dead," Mourinho said. "There are matches that look finished that aren't finished. The only explanation I can find is that they're easy games, we don't finish them off... it's a good thing that with the difficulty, the team reacts and wins, which is the most important thing."
Mourinho praised the contributions of Diomande and Espí, the latter of whom struck the winner.
"Espí is doing well, he's a lad with great motivation," Mourinho said, while praising Diomande's growth: "He's growing. He has very good work capacity and intelligence - it isn't easy to play 85 minutes on a yellow card. He's done a great job."
Asked about his side's defensive frailties, Mourinho said the issue stemmed from losing control of matches rather than a deeper structural problem.
"I like that my team scores goals, but I like to control matches, I don't like giving things away," he said. "They could score us a goal out of context, but today they arrived because we lost control of the game. Anselmi's team played very well, made good changes, and made life difficult for us."
Elche coach Martín Anselmi described feeling a mix of anger and pride despite the defeat, the third in a row for his side at home.
"Anger is the feeling I have. I'd take more pride from the performance and getting the result," Anselmi said. "It's not easy to finish off this kind of match."
He pointed to his side's growing maturity as reason for optimism.
"I'll take away the word maturity, we've matured like we did at San Mamés," he said. "We can compete against any opponent. We've competed, and the details haven't fallen our way."