The Welsh midfielder left Anfield for the Potters in the summer after failing to really force his way into Jurgen Klopp's plans.
Allen, 26, has performed impressively for Mark Hughes in the opening three games of the Premier League season while also scoring for Wales in their 4-0 World Cup qualifying win over Moldova on Monday night.
"I feel refreshed and really positive about the season ahead," said Allen.
"I think it had come to the point where I knew I needed to move on. Personally, it was pretty obvious.
"Hopefully I will get much more game time now and I think that is going to be really important for me in my international career as well.
"Any player will tell you regular football makes tonnes of difference to the way you perform and the way you feel out on the football pitch.
"It comes to a certain stage in your career where if it's not happening then you have to go and seek it out."