The Bluebirds revealed the kit Malky Mackay's squad will wear in their debut Barclays Premier League campaign on Wednesday.
The Puma kit featured two different shades of red, with the darker red being featured on the shorts; during their Championship-winning campaign the club's home kit had black shorts.
There was an overwhelming negative reaction to the new two-tone design on social media sites, and the club are to allow season ticket holders on the club's email database the opportunity to decide on whether it stays or goes.
A Cardiff statement read: "Cardiff City Football Club on Wednesday, May 29 launched the first images of the 2013/14 home kit, which featured two shades of red, the darker of which was carried in the shorts.
"The decision had been made as a means to help visually distinguish the club in the Premier League, while continuing the theme of our successful 2012/13 Championship winning season.
"The resulting response carried across social media quickly indicated that a large number of supporters were unhappy with the choice of colour concerning the shorts. For that we apologise.
"As a club, we would today like to address this issue by giving all 2013/14 season ticket holders held on our email database a vote on varied shorts options for next season.
"Although this will not result in every single season ticket holder voting, the size of the email based survey, reaching over 12,000 Cardiff City fans will give a clear indication as to the majority view."
Voting will start on Thursday and finish at 2pm on Friday; the club will then publish details of the winning option.
The club made the controversial switch from their traditional blue kit to red under owner Tan Sri Vincent Tan at the start of last season, while the club crest was also heavily altered.
Malaysian Tan, also recently denied reports he was considering further re-branding of the club, including a name change.