Starting their quest for a 10th European title after failing to reach the last eight the past six seasons, Real peppered Ajax with 36 shots at the Bernabeu but only Gonzalo Higuain marked his name on the scoresheet after Real's opener was credited as an own goal.
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Mourinho's Portuguese compatriot Cristiano Ronaldo and Argentina winger Angel Di Maria were especially profligate and the former, the world's most expensive player, was whistled by some fans.
Mourinho did not hide his frustration on the touchline, stalking up and down his technical area, clutching his head in his hands and at one point kicking out at the dugout. He was more philosophical after the match.
"I would be worried if we only had two shots or if (goalkeeper Iker) Casillas had been the best player on the pitch but he has hardly touched the ball in the last three matches," Mourinho told a news conference.
"It can happen that in a match when you play badly you score three goals and other times you can do everything on the pitch but score. The goals will come."
Mourinho, who joined Real from Inter Milan after leading the Italians to an unprecedented treble of domestic league and cup and Champions League last season, noted that he had only had 10 full training sessions with his players so far and the team was still under construction.
"Ten coaching sessions only together. With that number the development has been excellent and I am satisfied," he said.
Asked what he needed to do to improve shooting accuracy, he added.
"The best thing to do is nothing. Let them play. It's their natural habitat. One day a team will pay for it."
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