Edmond had made the comment Saturday after the Longhorns wrapped up spring practice with their annual scrimmage.
In a statement issued by the University of Texas athletic department Thursday night, Edmond said he apologized and expressed his respect for all Baylor has accomplished. He said he was just frustrated over being unable to play in last year's Texas-Baylor game and had "let all that anger build up and get the best of me." He concluded, "I won't let that happen again."
Edmond missed the 30-10 loss to the Bears with a lacerated liver. The victory clinched Baylor's championship and denied Texas its first title since 2009.
The teams meet Oct. 4 in Waco.