Fallon signed for Celtic, the team he supported in childhood, He remained first choice goalkeeper until the signing of veteran
Ronnie Simpson from
Hibernian in 1965. Fallon became the only Lisbon Lion not to play in Celtic's win in the
1967 European Cup Final against
Inter Milan, as he was the (unused) substitute goalkeeper. At that time the only substitute permitted was for the goalkeeping position. He was presented with a winner's medal by captain
Billy McNeill at a post-match dinner, but then had it taken from him in suspicious circumstances. According to his autobiography,
Keeping in Paradise (2015), manager
Jock Stein asked Fallon for his medal back. Fallon was then presented with a replica, while the real medal ended up with Celtic's chairman,
Sir Robert Kelly. As a result of winning the European Cup, Celtic entered the Intercontinental Cup later that year, a two-leg match against
Racing Club of Argentina. While warming up for the second leg, a brick (Robert Kelly said in his book,
Celtic that it was a "flat iron bar") thrown or catapulted by a member of the crowd, struck
Ronnie Simpson on the head. With Simpson unable to play, Fallon was called on to keep goal in a bad-tempered second leg, and an even more bad-tempered play-off. Although Celtic lost the return leg, and the subsequent play-off in
Montevideo, amid accusations of extreme foul play from the Racing players, Fallon distinguished himself with a string of saves which caused one commentator to remark: "If that's the reserve keeper, what must the other guy be like?" According to Kelly, when Celtic tried to get the second leg declared void because of the Simpson incident, Racing Club used Fallon's heroic performance as their counter argument, and the result stood. Fallon also played in the team that won the
Alfredo di Stefano Trophy, a testimonial for the
Real Madrid player. After Simpson's retirement, Fallon took over as first choice at Celtic. He lost his place to
Evan Williams due to a long illness, sitting out the
1970 European Cup Final. He left the club in 1971 and subsequently played for
Motherwell and
Morton before retiring from senior football. He later owned a pub in
Blantyre, where he had lived for many years. ==Later life and death==