The Ecuador international returned to Chelsea's starting line-up for the first time under Alonso in Saturday's emphatic 5-1 victory over Bournemouth, following a spell on the sidelines with injury.
Although Caicedo is already part of Chelsea's leadership group at their Cobham training ground, the 24-year-old knows he must become more vocal during matches to help his team-mates.
"With Xabi I am going to keep developing, for sure, and show him why he trusts me," Caicedo told Chelsea's official website.
He admitted that communicating more on the pitch remains an area of his game that needs improvement, despite his growing responsibilities within the squad.
"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," he said.
"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."
Caicedo also highlighted the influence of former Chelsea defender Thiago Silva, who set an example through his leadership and willingness to support his team-mates.
"You learn from the previous ones, like Thiago Silva; he was an example for us," Caicedo said.
"He tried to help us in every moment. How he was a leader here was amazing for all of us."
The midfielder is proud to be part of Chelsea's leadership group and understands the importance of setting standards through his performances, even if speaking up does not come naturally to him.
"Now being one of the captains is a pleasure for me, and a special feeling for my family," he added.
"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 are sixth in the Premier League table, eight points behind leaders Manchester City, and will aim to continue their progress when they travel to Everton on Saturday.
