The Bees defender has yet to agree a new contract and was left out for their first two Championship games.
However, the 26-year-old returned in Tuesday's 2-2 draw against Bristol City, with Nico Yennaris wearing the captain's armband.
"Harlee was excellent and he didn't need the armband to show he could lead," Smith told BBC London.
"I understand his reasons [for not signing a new deal] and I have no problem with that. I didn't feel it was right for the other players who are committed to the club that he carries the armband."
Dean, who is out of contract at the end of the season, has made more than 200 appearances for Brentford since joining them on a permanent deal from Southampton five years ago.
Brentford boss Dean Smith has praised Harlee Dean's leadership qualities despite stripping him of the captaincy.