It means Elokobi faces a three-game ban after being sent off for violent conduct following his aerial clash with Doncaster's James Coppinger.
Boss Mick McCarthy felt the challenge merited a yellow card at most from referee Anthony Taylor. However, the club have decided to accept the dismissal, which was the 10th red card the official had handed out in 19 games this season.
Club secretary Richard Skirrow said: "Having spoken to everyone involved, and having had another look at the incident which led to George's dismissal, we have decided not to appeal.
"We feel the red card received for the challenge was harsh. However, the referee's report talks about a reckless challenge which was late, at speed, and with excessive force."
Elokobi will miss the replay with Doncaster plus the league meetings with Manchester City (away) and Liverpool (home).
Source: PA
Source: PA