The two clubs were set to go before a Football League tribunal on Monday to decide the amount of compensation the Hornets should pay United for the striker.
However, Watford postponed the hearing because football operations manager Iain Moody is running the club's pre-season tour of Spain.
Carlisle have been assured the hearing will take place before the season starts on August 8, but United manager Greg Abbott was hoping to use some of the money to bring in a replacement for Graham.
"It is very frustrating because Watford have already done their business and left us hanging," Abbott told the News and Star. "I'm not sure it is good etiquette. They have chosen to do it that way but it leaves our club not knowing what money we are going to get from the sale, and I don't know how much I am going to have available for transfers.
"Watford haven't broken any rules but, from an etiquette point of view, it is not good for us."