Siena climbed five points clear of the Serie A relegation zone with the narrow win over a Roma side which set out to take the game to the home team.
However, the visitors struggled at times to break down the home defence and then fell behind to a goal after Emanuele Calaio converted a penalty early in the second half.
Calaio's spot kick turned out to be the match winner in the end as Roma were held scoreless by Siena.
"This was not our night, we made too many mistakes," Enrique told Sky Sport Italia.
"Many of our players were below their usual level.
"We always tried to attack, but if we do not control the ball it leaves us in trouble. It is clear we are still far from having the consistency that we are looking for.
"Siena were great in defence and they closed down very well."
The defeat was Roma's seventh of the campaign and leaves them in sixth position and one point behind Inter Milan who also lost 1-0 in their game with Novara at the weekend.