The two sides will now meet on Thursday, January 5 at 7.45pm after the game was brought forward 48 hours for live television coverage on Sky Sports.
Cook said: “The schedule for the Doncaster game is absolutely ridiculous. I want to go on record and say there has been no thought process for the fans.
“Well, I am looking at it from a fans’ point of view and think it is an absolute disgrace.
“For us as a team it is not the end of the world because we travel, it is what we do, we are paid to do that, it’s our job.
“But when you think Pompey fans have to go to Newport on Boxing Day, then to Yeovil, then at home to Luton and then travel to Doncaster on a Thursday night it is bizarre. Come on, give them a break.
“I wouldn’t change the games and I don’t see why Sky possess the power to do that.
“How many Pompey fans would we take up there on a Saturday if doing well? Then how many can go on a Thursday night?
“It is an attractive game in terms of the league table yet it is Christmas time, there is a lot of cost financially to families around that time. Now we have a game moved to a Thursday night from a Saturday. How does that help any of our supporters?
“But, sadly, it is where football’s at at the moment.”