Caicedo started his first game under Alonso following a spell out injured in Saturday's 5-1 rout of Bournemouth.
The 24-year-old midfielder is a member of the leadership group at the Blues' Cobham training ground but wants to make his presence felt on the pitch.
"With Xabi I am going to keep developing, for sure, and show him why he trusts me," Ecuadorian Caicedo told Chelsea's website.
"I think every coach tells me that I can improve talking on the pitch, you know? Because they know that I'm a leader, but it will be better for me if I start talking more with the players.
"I try my best, but it's not in my nature. So when I'm not able to talk, I just try to show even more.
"You learn from the previous ones, like Thiago Silva; he was an example for us.
"He tried to help us in every moment. How he was a leader here was amazing for all of us.
"Now being one of the captains is a pleasure for me, and a special feeling for my family. Even if I'm not a player who likes to talk a lot, I like to show through what I do, so others can see my example."
Chelsea, sixth in the Premier League table and eight points behind leaders Manchester City, travel to Everton on Saturday.
English Premier League
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