Connaughton joined the Manchester United groundstaff in January 1965, signing as an apprentice in May the same year. He turned professional in October 1966, but would have to wait almost six years for his United debut, despite playing three games for England youth in 1967 and 1968. In the meantime he was loaned to Halifax Town in September 1969, and to Torquay United from October 1971 to April 1972, both in the Third Division. He played two games for Halifax and 25 games for Torquay. His Manchester United debut finally came on 4 April 1972 in a First Division game against Sheffield United at Bramall Lane, a 1–1 draw. He played two further games that month, in defeats to Leicester City and Manchester City; the defeat in the Manchester derby came at Old Trafford.
Sheffield United
He returned to Bramall Lane in October 1972, but this time as a Sheffield United player, costing the "Blades" £15,000. He did not appear in 1972–73, and played only twelve First Division games in 1973–74.
Port Vale
Connaughton moved on to Third Division side Port Vale in May 1974, where he replaced Alan Boswell. He played 47 games in 1974–75, leaving deputy Reg Edwards to play just twice. For his consistency he was voted Player of the Year by the club's supporters. He missed just one game in 1975–76, with Manchester United loanee David Ryan covering him for a 2–1 defeat at Swindon Town on 17 January. He then faced stiff competition from a young Trevor Dance, but still managed to play 44 games in 1976–77. Connaughton missed eight games in 1977–78 due to a knee injury, but remained Vale's first team keeper as the club suffered relegation into the Fourth Division. He again suffered with injuries at the start of the 1978–79 season, however he lost his No. 1 jersey to Dance in January 1979, and played just 22 games in 1978–79. He spent much of the 1979–80 season on the bench, and played just nine games. He made 218 total appearances for the "Valiants".
Altrincham
He joined Altrincham in time to play fifteen league games of the club's Alliance Premier League championship winning 1979–80 season. He also played in the Conference LeagueCup final defeat to Northwich Victoria. He was an ever-present in 1980–81, as "Alty" retained their league title, and also beat Kettering Town in the Conference League Cup final. He also played in the club's 4–1 defeat to Liverpool at Anfield in the FA Cup Third Round. "Alty" dropped to eleventh place in 1981–82, though won one last success in the form of the Cheshire Senior Cup final, following a 1–0 win over Runcorn. He also helped the club to the final of the FA Trophy, where they lost 1–0 to Enfield at Wembley Stadium. He also helped the club to another FA Cup run, in which they beat former club Sheffield United and then York City, before being knocked out by Burnley. He retired at the end of the season at the age of 32, due to business commitments; he played a total of 127 games for Altrincham, winning 47 clean sheets.
Style of play
historian Terry Rowley described Connaughton as an "unfussy, dominant and quietly competent keeper".
Statistics
Source:
Honours
;Individual
Port Vale F.C. Player of the Year: 1974–75
;Altrincham
Alliance Premier League champion: 1979–80 & 1980–81