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The Giallorossi went out at the hands of Porto in a game that saw them receive two red cards, having also been reduced to 10 men in the first leg last week.
And the midfielder believes the squad must grow stronger as a result of the disappointment and now focus on throwing their energies into the league.
"We still created chances even after falling behind," Nainggolan said. "Just like in the first leg, we could have done more with 11 on the pitch.
"Trailing 1-0 with nine men, it's only natural you take more chances. We have to learn from these mistakes."
He added: "I think we're mature enough to avoid [the exit having a knock-on effect]. Now we'll dive back into league action.
"We'll be in the Europa League, maybe we'll go far in that competition and it could become a target but for now we have to concentrate on Sunday. We have to win in the league."
Despite the result, Nainggolan was one of a number of players to receive a rousing reception from the fans at the Stadio Olimpico as the nine men fought for every ball.
"Yes, I think we showed a lot of heart tonight," he added. "It wasn't easy with nine men although we even had a chance to equalise. Despite not winning, the positive thing is we gave everything."
Roma face Cagliari on Sunday.
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