Barkley has started the last four matches and he highlighted the strides he has made under the guidance of Sarri so far this season.
"I feel like in a short space of time I've developed really well," he told chelseafc.com.
"I feel as though I can still improve a lot. We're still getting used to our style of play and it's about repetition on a daily basis on the training pitch and transforming that into the games. It's going well at the minute.
"He believes in the team, he sees that we have a lot of potential to be one of the best teams in the world and be back in the Champions League and challenging for the major trophies. He has a lot of belief in me, a lot of belief in the rest of the team and that's good to see. It's always great to have the manager's backing, we're working hard on the training pitch and on matchdays."