Sarri demands more from Alonso and Loftus-Cheek
The left-back is one of seven players to have been nominated for August's Premier League Player of the Month award, having claimed a goal and an assist in his side's opening three wins of the season.
Alonso has also earned a recall to the Spain squad, having been overlooked for the World Cup this year.
Sarri, nominated for the Manager of the Month prize, is happy with Alonso's form but insists he can still sharpen up when the opposition have the ball.
"Alonso played very well in three matches," Sarri told a news conference. "I think he's a very good player and he can improve in the defensive phase. He's a very good player but I think he can do more.
"He has physical qualities at the top level, so I think he can do more in the defensive phase but I'm not worried. He's a very good player in the offensive and defensive phases, but I think he can do more."
.@MarcosAlonso03 is also an August Player of the Month nominee!
More https://t.co/HAi88XXTQE pic.twitter.com/ltYvFrRHUG
— Chelsea FC (@ChelseaFC) August 31, 2018
Another player Sarri wants to see more from is midfielder Ruben Loftus-Cheek, who has not played since the 3-0 win at Huddersfield Town on the opening day and was overlooked for the latest England squad.
"I can say I'm very happy with him, because in the last 10 days he has improved a lot," he said. "I'm really very happy with him. I think he will be important for sure. Starting in September, we will play every three days. He will be very important and very useful for us.
"I think so [he can push for a start]. It's not easy to play here because there are 25 very good players, so it's not easy to play in the starting line-up, but I think he will improve more.
"He has to improve, just in order to play my football. He has great qualities from a physical point of view, and technical point of view. I think he needs to improve from the tactical point of view, nothing else."
Sarri also expects Victor Moses to contribute more to the team once he has adjusted to being a winger rather than wing-back in the current system.
"He changed position on the pitch. We are trying to get him to play like a winger. We changed the position and in the new position; I think he needs to improve," Sarri added.
"I'm very happy with nine points from three matches, but now it's important to work, to improve more. We have the potential to improve more."
Chelsea host Bournemouth on Saturday.