Inter-county
Finnerty's hurling exploits in secondary school lead to an automatic selection on the Galway minor hurling team. He played against Tipperary in the All-Ireland minor final of 1982, however, he ended up on the losing side that day. Finnerty quickly graduated onto Galway's under-21 team, subsequently winning an All-Ireland medal with the side in 1983. His son Niall is one of the brightest football prospects in Galway at the moment. He is currently player of the Cortoon Shamrocks under-21 team.
That same year Finnerty made his senior debut in a National Hurling League game and he captured a place of his own on the team by the time the 1985 championship got underway. That year he played in his first All-Ireland final; however, victory went to Offaly on the day. In spite of this he was still presented with an All-Star award. In 1986 Galway reached another All-Ireland final; however, they were again defeated, this time by Cork. A second All-Star was collected by Finnerty. In 1987, in their third All-Ireland final appearance in-a-row, Galway took on Kilkenny. At the third time of asking Galway emerged victorious and Finnerty finally captured his first All-Ireland medal at senior level, before collecting his third All-Star award.[2]
In 1988 Tipperary were Galway's opponents in their fourth consecutive All-Ireland final appearance. Finnerty had another solid performance at wing-back and claimed his second All-Ireland title in the process, before later winning his fourth consecutive All-Star award. In 1989 Finnerty began the year by winning his first National Hurling League title; however, Galway's star centre-back, Tony Keady, was banned from playing for a year. The side had contemplated withdrawing from the championship in protest, however, they decided to play, eventually losing out to Tipp in the All-Ireland semi-final. In 1990 Finnerty played in his fifth All-Ireland final in six seasons. Galway were the hot favourites to beat Cork and it looked as if that prediction would come true when the tribesmen went 7 points up. Cork clawed their way back and eventually went on to win on a scoreline of 5-15 to 2-21. In spite of this loss Finnerty still won a fifth All-Star award.
Two years later in 1992 Finnerty missed the entire championship due to a cruciate knee injury. He returned in 1993 but could not command a regular place on the team. He did come on as a substitute in that year's All-Ireland final; however, victory went to Kilkenny. Finnerty regained his fitness in 1994 and played his last game against Offaly in the All-Ireland semi-final.