Three goals inside the opening 11 minutes settled the contest at the Bernabéu, and Funes was frank in his assessment of the damage.
"They pressed and they got the better of us in that spell of the first half. They're capable of making the difference and they punished us hard," he said, though he felt his side responded well after the break, reorganising their press and playing higher up the pitch.
"Either you're at your very best against a team like that, or the punishment is severe."
Funes was careful not to let the result at the Bernabéu, following an earlier trip to the Metropolitano, derail his side's broader outlook.
"I already warned this was going to be a marathon, not a sprint," he said, calling for emotional stability and urging his squad to focus on the visit of Levante next.
"We have to close this door and open the Levante one with excitement."
Still, he admitted he took no comfort from the scoreline given how much the travelling support had hoped for.
"You don't leave happy with a defeat, even knowing the difficulty of it," he said, pointing to a lack of daring on the ball as the main tactical takeaway. "When we had the ball, we lacked the boldness we've shown at other times," he said, calling on his side to be more aggressive in the final third and avoid becoming "fearful" or "a flat team."
Mourinho, by contrast, allowed himself satisfaction at a third straight win, while making clear he sees the club's start as the beginning of a longer process rather than a finished product.
"The second half was more about game management, a slower rhythm - Málaga had more comfort on the ball, but every time we accelerated, the feeling was always that another goal or two was there," he said. "Keeping a clean sheet was a target - you can't always attack with aggression, sometimes the opponent comes out and you have to defend well. Three important points."
The Portuguese explained his approach to squad rotation, with changes planned ahead of Wednesday's visit of Real Sociedad, and praised the contribution of Eduardo Camavinga, "a lad who isn't loved enough" but who delivered an excellent performance.
On summer signing Yan Diomandé, still finding his feet after a big-money move, Mourinho urged patience: "Normally when a player costs that much money, you expect them to arrive and explode immediately. But he's too young, and we need to be calm. He's doing very well, but little by little."
Asked about Dean Huijsen's development, he pointed to defensive solidity over technical flair as the priority, praising his central defender's growing conviction, while warning that adversity would eventually test the group.
"A bad moment will come. An important player will get injured, criticism will come, defeat will come. That's when we have to draw on all the strength of the team we're building."