Rosenior, 41, became the first Chelsea manager to win their first game in charge since Premier League winner Antonio Conte in 2016.
Chelsea were dominant throughout their win over Charlton, with five different players scoring the goals against the Championship side.
Speaking to TNT Sports after the game, Rosenior could hide his excitement, saying: "A good start, professional. I thought our first goal came at an important time in the game, it was a brilliant goal for Jorrel (Hato).
“The quality of my players was outstanding. Strong start, something to build on and quite a small game on Wednesday night!
"Goals change games and that comes down to quality of players. To get the goal when we did was really good. I've got a fantastic squad, I was delighted with the starting players.
“I thought Marc Guiu was magnificent, he deserved his goal. There are a lot of positives. Strong start but nothing to get too carried away about yet."
On how the team started: "I was delighted with Jorrel because it was a different role for him, he played as a 10 like Marc has done in the past and he gets the goal and does really well. I was delighted with Tosin and big Ben (Badiashile) at the back. Young Josh (Acheampong), full of potential, I was delighted with them."
On building on the win: "It's a busy two months. The lads have been really receptive to us and I thank them for that and if we keep working in this way I'm excited for the future."