His Slovakia manager, Jan Kozak, echoed the sentiment: "Football is a team game. Without support from your team-mates you can't really be a great threat to your opponents."
It was clear that Slovakia were keen to stress that there is more to Wales than just the supreme talent of the Real Madrid superstar.
But Bale is no ordinary talent. The electric forward is in a small bracket of players capable of winning a match on his own as evidenced by the fact he had a hand in nine of Wales' 11 goals in qualifying for Euro 2016.
It is no exaggeration to say that Chris Coleman's men would not even be in France without their brilliant talisman, who once more rose to the occasion with a stunning free-kick in Wales' crucial 2-1 win over Slovakia in their European Championship debut.
Not since 1958 have Wales featured at a major tournament and on that occasion a star-studded Brazil side, including the legendary Pele, proved their conquerors in the World Cup quarter-finals.
Few would back Wales to be among the contenders for glory in France, but in Bale they have an extraordinary weapon that can certainly help them spring a few surprises on their way.
That was evident by his opening statement on the big stage after just 10 minutes. Bale lined up a free-kick right of centre, though he struck towards the opposite corner, the dip and swerve on his effort completely bamboozling Slovakia goalkeeper Matus Kozacik.
There was a certain poetry about the goal. 10 years earlier, against the same opponents, Bale opened his Wales account at the tender age of 16, again via free-kick.
Much has changed since then for the poster boy of Welsh football. He is now a leader, a galvaniser and a world-class talent. Any doubt that Bale could freeze on the big stage was quickly evaporated.
But Hamsik was right about one thing. This was not an individual victory, Bale versus Slovakia. The supporting cast played their part as well.
Slovakia's tactics became somewhat brutish and Ondrej Duda levelled the game 52 seconds after coming on as a substitute, but having weathered a brief storm Wales regained their composure.
Arsenal midfielder Aaron Ramsey still has plenty of doubters and was not always convincing in Bordeaux, but he made a crucial impact by laying on the winner for another unheralded Welsh hero Hal Robson-Kanu.
Unlike so many international sides, Wales look like a team, a squad that will lay everything on the line for one another.
But at the heartbeat of that side is Bale, one of the world's best. The Euros is a better tournament for his presence.