The Blues were comfortable 7-0 winners on Saturday.
With Reece James and Enzo Fernandez unavailable, Palmer took on the captaincy for the day.
"Long time coming," Palmer said afterwards. "It was a proud moment being captain. I enjoyed it and it was a good afternoon."
He continued: "We needed to win. It was a difficult four games (before the international break) but to get to a semi-final at Wembley was very important.
"It’s nice to see everyone getting involved (with the goals) and laughing, joking and smiling after the game.
"I think it will give everyone a lift. Playing, winning and scoring goals is good for everyone. Getting back to that winning feeling was nice and hopefully we can take that on to Manchester City."