Coleman, a junior and the team's second-leading scorer, was ejected after stepping on Budinger's face following a charge call with 9:51 left in the second half. Arizona rallied for a 96-90 win in overtime.
"I want to apologize to Chase Budinger for what happened Saturday night. I never meant to step on him," Coleman said in a statement issued by the school. "I have never been in an incident like this before, and I have nothing but respect for him as a great player.
"I love the game too much to do something like that intentionally. I want to say I am sorry from the bottom of my heart," Coleman said. "I know that God knows what is in my heart, but I am hopeful that Chase will understand and forgive."
Houston coach Tom Penders said he regretted the incident but does not believe Coleman intentionally stepped on Budinger.