The Spanish coach criticized the midfielder's commitment before the match and refused to say whether he will make the squad for the match against Lazio.
The 28-year-old midfielder sat in the stands during the match despite not suffering any physical problems, with reports suggesting he had arrived late for the team's meeting on Sunday morning.
"I do not talk about what happens in our dressing room or in our team meeting," Enrique told Sky Sport Italia. "The squad always comes before individual players and I am sure that what I did was right if analyzed in the medium-long term.
"De Rossi did not seem prepared to play and that is why I left him out. This defeat did not happen because one specific player did not play. If I could go back in time, I would make the same decision. I need everyone to feel responsible, especially the players who are important to this group and this club."
Enrique then refused to blame the result on the rearguard, as Roma could not stop Atalanta's counterattacking football.
"When we are talking about a defensive problem, we are talking about the entire squad," he noted. "We want to have a high possession of the ball and for this we must play with two center backs in the opponent's own half.
"But today we did things wrong and we were left exposed to their counterattacks."
Questioned if De Rossi will make Roma's squad for the upcoming match against cross-town rival Lazio, Enrique was noncommittal.
"I will let you know," he said.
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