Evan Ndicka and Gianluca Mancini had Roma 2-0 ahead before Nice pulled a goal back with almost 25 minutes to run, but the visitors held on for the three points.
Gasperini said afterwards: "We've played a lot of games now, and we have this characteristic that makes it difficult to get shots on goal. Aside from that untimely incident, several players performed at a high level.
"We had some problems towards the end, especially with the substitutes: we always have the right mentality, but we struggled a lot tonight too."
With two defenders scoring, Gasperini also said: "We need to see our entire attacking side improve, without focusing too much on the centre forward.
"(Artem) Dovbyk is improving physically, we need to improve everyone to allow the attackers to be more dangerous by putting them in the best possible conditions."
On Nice's penalty, he added: "In football, a single incident is enough to turn a game around, and you have to see it through to the end. This avoidable incident happened tonight, but we have a very solid and competitive core; we just need to integrate it by learning from the players who are used more consistently."