Carey made his 646th appearance for the Robins when sent on as a late substitute during the 4-1 home victory over Stevenage, beating the tally of the late John Atyeo - an England international striker.
"It's a record that will never be broken again," said City boss Cotterill. "You don't play that many games without being a very good footballer and Louis is a very good person too."
Greg Cunningham headed Bristol in front from a Scott Wagstaff cross after seven minutes and skipper Sam Baldock made it 2-0 with a close-range finish from Jay Emmanuel-Thomas's cut-back five minutes later.
But it took some fine Elliott Parish saves to preserve the lead before Emmanuel-Thomas netted twice in quick succession either side of the midway point of the second half.
The big striker took his goal tally for the season to 17 by converting a low Baldock cross and then lashing the fourth home from the corner of the box after a strong solo run.
Stevenage striker Francois Zoko fired a 74th-minute consolation but it was too late to prevent City from recording back-to-back league wins for almost 12 months.
A delighted Cotterill said: "It was nice to give our fans something to cheer at the end of a difficult year.
"We are passing the ball better as confidence grows. I still hope to be busy during the transfer window but it's always best to integrate new players into a winning team.
"We have created a lot of chances in every game since I took over and we managed to convert a lot of them in this game.
"There is still a lot of work to be done, but the players are responding well to what is being asked of them."