Barkley impressed for the 1-0 win.
"I felt good out there," Barkley told the official Chelsea website. "We have been working for the last couple of days on tactical work and I have worked hard during the off-season. In this game I felt really strong and I am ready for the season ahead. Game by game I will feel much better and ready for the season.
"I came through a difficult spell with a few little niggles after a long-term injury but now I feel as strong as I have ever felt before," he added, "and I am feeling fitter than I have every felt so yeah, I feel good."
Barkley played different roles during the game. In the first half he was one of the more advanced midfielders along with Cesc Fabregas, with Jorginho playing deeper, then in the second half he operated on the left of the attacking three.
"As a young player breaking through at Everton, that is the position I played in," he says of the second of those. "I was in that position because it gave me freedom to express myself and I understand that role, and I understand the other roles in midfield so I am happy to play anywhere as long as I am on the pitch.
On manager Maurizio Sarri, Barkley added "The style that he wants us to play, it is really exciting and very attacking, as well as being very organised. We have been understanding what he has been getting across in training but the more we do it in training, the more we get used to it and I can see from the training sessions that this season is going to be very exciting."