Carsley opted to pick Ollie Watkins over Kane for Thursday's away clash, leaving right-back Kyle Walker to don the captain's armband in the absence of the Bayern Munich striker.
Watkins wasted little time in indicating Carsley's decision, with the Aston Villa forward scoring inside the opening 10 minutes in Athens.
That early strike gave England a slender half-time lead, before they extended their advantage courtesy of an Odysseas Vlachodimos own goal and an inventive Curtis Jones flick.
Carsley reveals reason behind Kane omission
Kane ultimately had to settle for a substitute role, with the Bayern forward coming off the bench to replace Watkins in the 66th minute.
The 31-year-old earned his 102nd international cap, but England's all-time record scorer was unable to add to his 68-goal tally.
Prior to the game, Carsley revealed that he decided to pick Watkins over Kane to give the Villa striker the chance to gain valuable experience on the international stage.
"It was important to give Ollie Watkins an opportunity," Carsley told ITV ahead of kick-off. "To experience a night like this will be great for himself. This team needs to try and create leaders and one way to do that is give them opportunities."
When asked how Kane handled the news, Carsley said: "He is fine. He wants to play but his attitude has been fantastic."
Kane's omission follows controversial comments
The decision to drop Kane would not have improved his mood after he previously expressed frustration with the recent flurry of withdrawals.
Kane admitted it was a "shame" to see a whole host of players withdraw from the squad ahead of Thursday's trip to the Greek capital.
The England captain will now have to wait to see if he is selected in the starting lineup for the final game of Carsley's interim tenure.
Carsley will take charge of Sunday's home clash with the Republic of Ireland, before he hands over the reins to England's new permanent manager, Thomas Tuchel.
The Three Lions will enter the final matchday in top spot of their UEFA Nations League group, with goal difference giving them the advantage over second-placed Greece.