Atkinson has been put in charge of the Toffees' FA Cup fifth-round tie at Bournemouth but has recent history with the club from when he took charge of last month's controversial Capital One Cup semi-final with Manchester City.
Officials failed to spot the ball had gone out of play before Raheem Sterling crossed for City's second goal and Jagielka's complaints, he claims, were met by a sarcastic comment from the referee.
Jagielka, who labelled Atkinson "a little bit arrogant" in his attitude after the game, will now come face-to-face with the Bradford official this weekend.
"There is nothing much we can do, is there?" Jagielka told the Liverpool Echo
"We've had him before and we'll have him again.
"I stick by the things I said, especially in a semi-final game, but we'll get on with it, shake hands and deal with the day.
"He's been a good ref over the years but I said what I felt after the game and, to be honest, I did well to probably hold most of my emotions back.
"Everyone makes bad decisions but you have got to look at the context of the game.
"You have got to look at scorelines and you have got to adapt your mannerisms throughout the game.
"If someone is going to shout and bawl at you, by all means don't speak to them, but in the big games when things are on the line you have got to show the respect both ways.
"If he thinks I've over-stepped the line then pull me to the side and say 'That's it', that is fair enough.
"But it's difficult when you go out there and within two or three minutes of the game you're at that stage already, where you've not said or done anything, and some officials are like that.
"Whether you've got their back up from previous games, I don't know, but it is a difficult one."
Source : PA
Source: PA