La Roja peppered the opposition goal with 21 shots, with eight of them hitting the target, but were unable to find their elusive opening goal.
They dominated with 72% of possession, too, but were done by a 76th minute sucker punch by Viktor Tsyhankov, who burst through on goal to take advantage of some questionable positioning from De Gea to fire a strike into the right corner.
It appears as if the Man Utd keeper is expecting the ball to run through the middle, only for Tsyhankov's touch to take the ball to the right, leaving a huge gap at the near post.
Enrique, however, has warned against the "habit" of continually blaming De Gea.
"You can always do more, but blaming De Gea is already a bad habit," the Spain head coach said after the defeat.
"If David is blamed for a game like this, switch it off and we'll leave."
Enrique concedes that the winning goal came about due to Spain's constant pressure, as they were suddenly left on the backfoot when Ukraine sprung free with a rare counter.
"If you attack in a continuous way, you know there are transitions. If a team defends and keeps it at 0-0, they grow, and in one action they've caught us. We have to congratulate them," he added.
De Gea has received criticism for his performances at club level with Man Utd recently, too, with some fans and pundits calling for him to be dropped in favour of Dean Henderson, who impressed last season on loan at Sheffield Utd.