The Wales international is looking forward to his Anfield debut against Roberto Mancini's men and is hoping for a good result after an opening day defeat
Brendan Rodgers suffered a dismal start to his Liverpool career with a heavy defeat, in a game which also saw Daniel Agger sent off.
Yet the Reds face a busy week, traveling to Hearts in the Europa League on Thursday before welcoming City to Anfield, and Allen is looking forward to the challenge.
“It was brilliant to make my debut. It wasn't the ideal debut in terms of the result, but it was one of those days that didn't go for us and we have to move on from that,” he told the club’s official website.
"It could be a very special week for me, getting the chance to play in Europe for Liverpool and then hopefully my Anfield debut against Manchester City, and we hope at the end of both of those games it will be a nicer feeling. We will certainly give everything we have got for our supporters."
Allen also claimed decisions had gone against the Reds in the defeat to West Brom, but backed his team to be ready for the next game against Hearts.
“They scored a fantastic first goal and that was one when sometimes you have to hold your hand up and say it is a great goal and there's not much we could have done to stop that,” he added.
"The first goal certainly gave them a foothold in the game and then with the decisions that went against us, and going down to 10 men, it changes everything.
"Throughout the season there is going to be some days like this and we will regroup, work hard in training and get ready for Thursday's game."
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