[1] In his first nine matches for Australia, he scored eleven goals all coming from the 1967 South Vietnam Independence Cup.
Attila played his senior debut for Melbourne Hungaria in 1962 at 15 years of age in the old Victorian State League.
In that same year Abonyi was man of the match in helping Melbourne Hungaria win the Australian Cup, with a hat-trick, to defeat the favoured APIA Leichhardt 4–3 in extra-time.
In June 1975, Abonyi made a guest appearance for a touring Manchester United side, coming on as a substitute for David McCreery against Queensland.
[5] Abonyi was well known for being a member of the Australian 1974 World Cup squad in West Germany and also represented New South Wales and Victoria.
Abonyi then moved to Melita as a coach only, where they won the minor premiership and lost the grand final.
[13] Abonyi made a lap of honour on the MCG at half time of the 1998 World Cup qualifier against Iran.