Ahead of Friday's clash with the Scots at Cardiff City Stadium and the match against Croatia in Osijek, the Dragons are bottom of Group A having lost their first two fixtures – a 2-0 home reverse to Belgium and then a humiliating 6-1 drubbing in Serbia.
Those results last month extended Wales' losing streak since Coleman was appointed as successor to the late Gary Speed to five games.
But when asked if he felt the right man was at the helm for Wales, Allen said: "Yes, of course.
"We are all with him. He is a fantastic manager and the preparations have been perfect for us.
"It has all been set out the perfect way for us to play football, and as players we have to shoulder responsibility now when we get out on that pitch and make sure our performance levels are at the standards they should be."
Although they are yet to register a point after two matches, Wales are only four points behind Croatia, Belgium and leaders Serbia in Group A, while Scotland have two points and Macedonia one.
Allen feels it is vital the Dragons show a reaction after what happened in Serbia and is confident they can claim a victory on Friday to kick-start their campaign, although he is not about to refer to the Scotland contest as a must-win game.
"After a disappointing defeat you always want to bounce back as quickly as possible, so luckily this game has come around quite quickly," the Liverpool player said.
"But we have also had time to reflect. We have to make sure we put things right.
"It is not all over. You have to be confident and faithful that you can still achieve qualification. That is our one and only aim."