"It was a difficult decision to cancel the deal," said City chairman Stephen Vaughan.
"We don't make any money from the agreement when all the expenses are deducted, but the main reason is that I'm extremely saddened that a promise to play a pre-season friendly match hasn't been honoured by Liverpool.
"The original reason given to us for the cancellation of the fixture was that Liverpool were contracted to participate in a foreign tour, but I've learned through a friend in the media that they were to play a friendly at our neighbours Wrexham.
"That information was the straw that broke the camel's back."