Floyd, Enfield and other members of their coaching staffs exchanged heated words Wednesday night as months of back-and-forth between the programs came to a head.
Enfield said he was reaching out to Floyd, who coached USC from 2005 to 2009, to apologize when the mood immediately soured.
On Thursday night, Floyd appeared unlikely to accept any apology but said he was moving on.
"I don't see any reason why we'd talk [in the future]," he said. "It's over with, that's for sure."
The feud began in April, with Floyd calling Enfield because he thought USC was tampering with UTEP recruit Isaac Hamilton (No. 32 in the 2013 recruiting class, according to ESPN's RecruitingNation).
"I lobbed a call into Coach Enfield back in April and felt like there was tampering going on with [Hamilton], and sure enough, three months later he put USC on his Facebook page and backed out of his letter of intent," Floyd said Thursday. "I called and we discussed that in a very serious vein. [Enfield] asked me not to turn him in, and [he said] that they just wouldn't take [Hamilton]. But we didn't end up with him, and that was a lick."
Hamilton sought a release from his letter of intent in July. Floyd initially denied the release while accusing Enfield and USC of tampering. The former McDonald's All-American eventually was granted a release and enrolled at UCLA, where he will sit during the 2013-14 season after his waiver request was denied by the NCAA.
The feud escalated when Enfield criticized Floyd in a Men's Journal article that was released last week.
"Tim Floyd shows up every day at work and realizes he lives in El Paso, Texas," Enfield told the publication. "And he's pissed off that he didn't get the USC job two months ago. I told him, 'Tim, if I could have all this power to somehow convince a family to do this, why the heck didn't the kid come last spring, when I first got the job?' "
Floyd responded Thursday
"I damned sure didn't appreciate the comments that he made last week publicly about the city of El Paso, Texas, where my grandparents were born and raised, where my father was born and raised and played at Texas Western, and where I lived 22 years of my life," Floyd said Thursday. "It's a fabulous city, and my reaction yesterday was more about the city of El Paso than the previous part."
Floyd added, "As far as him saying he was just trying to apologize yesterday, it would've been really nice if he had apologized three weeks ago when that magazine article came out. His timing wasn't very good."
Enfield expressed regret Thursday for the incident.
"I regret that the situation happened and I apologize to the USC fans, but this is about the players," Enfield said. "We're moving on."
Pac-12 commissioner Larry Scott is in contact with USC to get an understanding of what occurred between Enfield and Floyd, a conference official told ESPN on Thursday.
The official said it was primarily a school issue and did not say whether Scott would take action upon learning of the full scope of events.
"I'm not going to have any more comments down the road, but we're not going to sit back and just take it in the shorts," Floyd said. "We're just not going to do it. We've done it enough."
ESPN's Myron Medcalf and Andy Katz and The Associated Press contributed to this report.