Alexandre Lacazette's late strike condemned the Giallorossi to a two-goal loss, despite being 2-1 ahead at half-time.
Jesus rejected suggestions his teammates had tired in the second half, blaming mental failings. But he believes the tie is far from over.
“They attacked better, but it was an open game and it was important to get two goals over here," Jesus said. "Now we need to learn the right lessons from this result and do better in the return leg.”
He added: "In a game like this, you need to be 100% focused all of the time and today, unfortunately, we didn’t quite manage that.
"Either way, we need to think about the next game now. Everything is still open. We’ll go home with this result and we’ll have to do better at the Olimpico.”
Now the Giallorossi must produce a stirring display at home if they want to progress.
“I don’t know whether it’ll be 2-0 or something else," he said. "But in Rome we have to win and make sure we get to the next round because it’s important for our season as a whole.”
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