The Spanish dominated their Nations League match with Ukraine but lost 1-0 to a second-half strike with the Manchester United goalkeeper caught off his line.
It is the latest error made by De Gea in recent months but Enrique feels that blaming the keeper is a "bad habit".
Speaking after the game, he said: "You can always do more, but blaming De Gea is already a bad habit. If David is blamed for a game like this, switch it off and we'll leave."
Enrique credited Ukraine for staying in the match and knew his team were vulnerable to a twist with the scores level at 0-0.
The former Barcelona boss said: "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.
"Nothing happens because in one or two games you don't score goals. We created chances to kill them off. It was a game clearly under our control, with opponents closing the passes and the passing lines.
"We created chances with Adama [Traore] through his overlapping. In the end, we went into panic mode. I've lost lots of these games in my career. The opponent is growing and then in a transition…
"The conclusion is I liked the attitude of the players. I like what I see."