Donyell Malen's hat-trick, laid on three times by Paulo Dybala, gave AS Roma a dominant start under Gasperini, with Niccolò Pisilli completing the scoring late on to leave Fiorentina's new era under Grosso with an immediate reality check.
Grosso was left to reflect on a night his side never got going.
"We came up against a strong, settled team that showed the same level as last year. I knew it would be difficult — we conceded the first goal from a dubious passage of play, then we conceded the second at the worst possible moment.
"We're disappointed, but our opponents put us in difficulty. We'll take plenty from this and work to improve," he said.
Asked about his selection choices, including starting Moise Kean from the bench, Grosso explained his thinking.
"In a game like this, it's reductive to talk about individuals. On Kean, I expected a match where you'd have to get your hands dirty — we could have started both strikers, but it would have unbalanced us too much. So I preferred Mateo, who battled well, and I wanted to bring on Kean's qualities in the second half. While I was making the change, we conceded the goal."
He was candid about the scale of the task ahead.
"We have to work a lot, there's a lot to improve. Coming here, against a strong team, is never easy. It's not enough just to work hard, you also have to play full matches — when there's defending and battling to do, you have to do it."
For Gasperini, the performance underlined a squad now settled into its second season together.
"I'm very happy — this is an extraordinary group. We built a foundation a year ago, then added quality. Now the group is settled, the new arrivals are functional, and that's important. As a result, today's start was very positive," he said.
He singled out the impact of his front three, including debutant Rodrigo Mora alongside Dybala and Malen.
"They're world-class. Dybala has always been that, he's just had one injury too many. This man is a beast — forget the 'silk muscles' people used to talk about, he can play extra time if needed. Last year he was unlucky, getting injured taking a free-kick and a penalty.
"Malen is extraordinary, but it's no coincidence — he feels appreciated and strong, he's a leader on the pitch and can still improve. What he's showing is incredible, he seems to have found the right environment."
On Mora's contribution specifically, Gasperini added: "When he touches the ball, something beautiful happens. We need to give him continuity, but he has top-level qualities."
Asked about Manu Koné, who requested to be substituted, the head coach explained: "I pushed him a bit, he only arrived recently after the World Cup. There's a gap in condition between those who went to America and those who didn't, but he went beyond that with his generosity and rightly asked to come off. He played very well, he just needs to train and find his sharpness again."