Mills played for a local village team before being spotted by a Nottingham Forest scout at the age of 11. Aged 14 he broke into Forest's reserve team, which played in the Central League. Mills also played for Long Buckby's youth team, and was part of the team that won a national under-16 competition. He started his senior career at Forest under the management of Brian Clough, making his first-team debut in a 2–1 victory at home to Arsenal in the First Division on 9 September 1978, and in doing so became Forest's youngest league player at the age of 16 years and 203 days. Mills signed a professional contract with Forest on 13 November 1978, two days after his 17th birthday, after serving his apprenticeship He scored his first goal for Forest with the opening goal of a 2–1 win away to Leeds United on 15 May 1979. Despite not participating in the 1979 European Cup Final at the Olympiastadion, in which Forest beat Malmö FF 1–0, Mills became the youngest player to win the European Cup at the age of 17 years and 201 days on the virtue of having made one appearance in the competition that season. He finished the 1978–79 season, in which Forest were First Division runners-up, with six appearances and one goal.