Coleman's team came from behind to secure their first three points of the World Cup 2014 qualifying campaign, courtesy of a brace from Tottenham winger Gareth Bale.
Despite being only nine months into the job, Coleman's future at the helm of the national team has been called into question after a string of poor results including a 6-1 thrashing against Serbia.
But Allen insists that the players are fighting for their boss - and their performance during the victory against rivals Scotland illustrated just that.
"It's a massive win for the manager," Allen told reporters. "We, as players, spoke about how our performance wasn't good enough in Serbia.
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"We're fully behind the manager and the performance speaks volumes of our faith in him. It's about time that we got three points for him."