Claude Bassett made the admission during a live interview on WKYT-TV. He previously denied any knowledge of the money orders or payments to Melrose High School coach Tim Thompson.
"I just felt it was necessary to stand up and look people in the eye and tell them what I did," Bassett said.
"Bottom line, to all the fans and to all the people that I have caused any undue hurt, I fully apologize. I know that doesn't mean much to some people, but right now it's about the best I can do."
The Courier-Journal reported last week that it had obtained copies of four cashed money orders totaling $1,400 purchased Oct. 25 at the University of Kentucky Federal Credit Union and made payable to Thompson.
On each money order, Thompson's name was written by hand into the space designated for the payee.
The newspaper also reported that it had obtained a copy of a U.S. Postal Service Express Mail address slip showing that an item was sent by overnight mail on Oct. 25 to Thompson with a return address from "Claude Bassett, Commonwealth Stadium, Lexington, Ky."
Thompson is the head coach at Melrose, a Memphis football powerhouse, and had been reported to be a candidate for a vacancy on Kentucky coach Hal Mumme's staff. Thompson has denied receiving or having any knowledge of payments from anyone associated with the university.
Bassett until recently coached Kentucky's kickers and punters. Following the Wildcats' 2-9 season, Mumme fired five assistants, including Bassett.
Bassett said during the television interview that no other school officials including Mumme and athletics director Larry Ivy - assistant coaches or players had any knowledge of his actions.
"I was given a great deal of trust, a great deal of latitude to do certain things to try to build this program right, wrong or otherwise," he said. "Whatever my intentions were, I did wrong things. I did things that were not appropriate and certainly not endorsed by anybody.
"I did these things on my own. The acts were stupid and foolish, but nonetheless they were committed, and I felt it necessary to come and speak to people and let them know that I had in fact done these things and cooperated fully with the university. This does not need to go on."
Neither Bassett nor Mumme could immediately be reached for comment by The Associated Press.
"We appreciate Claude Bassett's willingness to meet with us and his cooperation with our internal review of our football program," Ivy said in a statement released Friday night. "We will have no further comment until our review is completed and submitted to th NCAA."
Prior to Bassett's interview, Ivy had said Kentucky's internal investigation could be wrapped up as early as next week.
The school's initial probe began last month following reports that Thompson and three of his players received improper benefits during a recruiting visit Nov. 3 and 4. Those benefits allegedly included free lodging and jackets given by the school to wear during a game against Mississippi State.
Allowing recruits to keep merchandise such as jackets is not allowed. Under NCAA rules, schools can pay for a recruit's lodging during an "official" recruiting visit, but the Melrose players in question were on "unofficial" visits that weekend.
Ivy had said that after speaking with Bassett and Thompson last month, he was assured that the players had returned the jackets, and that Thompson had paid for the hotel rooms. The next day, however, he announced he was going to investigate the matter further.
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