The Swiss team only need a draw to make it of Champions League Group B, while the Reds need all three points.
But Allen is confident his side can produce the goods - mainly due to the support of the Kop.
"It's a great position to be in to have fate in our own hands, we know what we have to do and will give everything," the Welshman told reporters.
"We'll draw inspiration from previous games, the support will be a huge factor and we will make things as difficult for Basel as we can.
"We learnt a harsh lesson in the away leg and certainly will not underestimate them.
"We learnt a lot from last year. We can use the experience to help us, we were confident when the draw was made we could qualify and nothing has changed. We've just got to make sure we get the job done."
Liverpool host Basel at 7.45pm on Tuesday night.