The Chelsea captain was speaking after leading the Blues to a 3-2 victory at the Stadio Diego Armando Maradona on Wednesday night, a result that sealed qualification for the Champions League Round of 16.
It marked James' 50th appearance as captain and came after Chelsea fought back from 2-1 down in one of Europe's most demanding atmospheres.
Enzo Fernandez converted a second-half penalty before Joao Pedro struck twice to complete the turnaround and ensure Chelsea avoided the knockout phase play-offs.
"We're progressing, we're learning, we're adapting, and we're evolving with every opportunity we get," James said. "I think we showed that against Napoli.
"Napoli is always a super difficult place to come. It's an amazing stadium with an amazing atmosphere. The game was difficult, but it's a huge step in the right direction.
"It was a special performance from a special group. It's a super tough place to come and win, especially when they're leading. I think that was a statement win."
Rosenior surprised many by deploying James at centre-back, having previously used him at right-back and in midfield this season. The 26-year-old said he is enjoying the challenge of adapting to the new manager's demands.
"When a new manager arrives, there's a different style of play, and everyone is adapting and trying to learn as quickly as possible," James added. "The results speak for themselves.
"It's still early, but every session and every game we're improving."
James also praised Cole Palmer after the midfielder made a decisive impact from the bench, setting up two goals after coming on at half-time.
"Cole has been through a difficult period with a few setbacks," James said. "We're super happy to have him. He showed what he can do, even in just 45 minutes.
"Everyone needs to stay patient. He's an amazing player and still super young."
Chelsea return to domestic action on Saturday when they host West Ham United at Stamford Bridge in the Premier League.