Demarai Gray and Jamie Vardy struck to seal a gritty 2-1 win over Brighton as Rodgers watched from the stands at the King Power Stadium on Tuesday night.
The 46-year-old signed a deal until 2022 after joining from Celtic earlier in the day. Davy Propper pulled a goal back but Leicester hung on to rise to 10th in the Premier League.
"He's just come into the dressing room after the game. He was very positive, bouncing. We're all desperate to start working with him," Stowell said.
"He said before that he was just going to leave it and observe from up there. He said call the subs yourself and just get on with it but he's going to bring something special to the club.
"He spoke to the lads and the lads were in awe listening to him. He said 'I've only left to come here for one reason and that's to work with this group of players'. That speaks volumes for this young group of players.
"We're going to have a meeting to outline what he expects from us (coaches) and he'll have the players on Thursday and we'll go from there."