[1] Puckett began his career with Southampton during the 1970s and played nearly 100 games for them in the First Division between 1978 and 1986, scoring 14 times.
[1] Puckett suffered a major knee injury while playing for the Dean Court side and was loaned to Aldershot in the 1988–89 season, scoring a hat-trick on his Third Division debut for the club, and was soon signed on a permanent basis, but was unable to save the Shots from relegation.
[5] He made fifteen league appearances for Totton & Eling, scoring one goal.
[6] On 21 May 2014 Puckett played a 4th division game in Iceland for Hvíti Riddarinn (The White Knights).
Puckett was substituted in to the game in the 66th minute along with his son Bill who is one of two coaches of the team.