In a phone interview with ESPN, Dineen called the ploy to send a message to Mayfield and the Sooners "a dumb impulse decision."
"That's not how this game should be played," Dineen said. "It won't happen from me or from this program again."
As tensions on both sides escalated after the coin toss snub, Mayfield grabbed his crotch and appeared to yell "F--- you!" at the Kansas sideline during the third quarter.
On Monday, Oklahoma coach Lincoln Riley announced that Mayfield wouldn't serve as a captain in the Sooners' regular-season finale against West Virginia because of his actions. Riley also said Mayfield, a senior, would not start in his final home appearance with the Sooners.
Also on Tuesday, the Big 12 announced a public reprimand of Mayfield for his actions.
"Mr. Mayfield's actions are unacceptable and should not be tolerated," commissioner Bob Bowlsby said in a statement. "I am grateful for the efficient management of this matter by the coaches and administration of the University of Oklahoma. Baker Mayfield is a truly outstanding competitor and I generally appreciate his style of play and the manner in which he competes. However, the behavior he exhibited on the sideline during the Oklahoma-Kansas game was inappropriate and contrary to our sportsmanship policies."
The conference also reprimanded Dineen, Wise, Armstrong and Jeremiah Booker for not shaking hands with Mayfield.
"The refusal of these student-athletes to shake an opponent's hand during the pregame ceremony is contrary to tradition and inconsistent with common courtesy," Bowlsby said in the statement. "The pregame handshake among team captains is symbolic of good sportsmanship. This breach of protocol is not in keeping with the standards of the Big 12 Conference. I am grateful for the work of the Kansas administration and coaches to resolve this matter."