Peters wasn't grinning from ear to ear, but was "fairly happy" with the final outcome.
"It's always good to get the win, but we know we have better teams coming in," he said. "We've just got to continue to get better. I don't think we're where we need to be at this point in the season, but we'll take this win and move forward."
Peters finished with five tackles, including one for a loss of three yards.
Kentucky senior linebacker Micah Johnson, who led the Cats with 12 tackles, including one for a loss and one quarterback hurry, said Peters was at the right place at the right time down the stretch.
"He made a big play when we needed it," he said. "It was a great play on Corey's part and Sam's part. Corey is a great player and he's a leader on this football team."
In a game dominated by the Cats in the first half, Peters and the team's defensive unit held its own in the third quarter after the Cats committed three turnovers and ran just four plays to open the second half. The Cardinals connected on two field goals and missed another in the third quarter. All three possessions by Louisville left Kentucky on the edge.
"It was a very ugly game, especially in the third quarter," Peters said. "We really had an opportunity to end the game at that point when we should have. We were put in several bad positions on defense, but we held them to field goals the first two times and I'm happy with the aspect that we never gave up. I think we are a mature team compared to some of the other (UK) teams of the past."
Although the third quarter wasn't pretty, Peters said the team didn't give up and "kept fighting" down the stretch. Peters said the ability to come back and get the win in the fourth quarter spoke of the team's overall maturity and focus.
"There were times in the fourth quarter it was going back and forth and we could have easily hanged our heads, but we kept fighting and we made the stops when we needed to, which we needed to make a little bit earlier, but it is what it is," he said. "I'm happy with the win, but we need to go back to the drawing board."
Heading into Saturday's showdown against top-ranked Florida, Peters said the Cats can't afford a third-quarter lapse and put the defense at risk.
"I think everybody pretty much understands that we have to play better to hang with the upper echelon teams in the SEC," he said.