Barnes and James Maddison struck in the 2-0 win on Saturday.
“I think it panned out the way we thought it would," the one-cap England international said. “It was a difficult game.
“We were happy to go in at half-time ahead, but we weren't particularly happy with our performance.
“We thought we were a bit off the pace, but I thought in the second half, we were a lot better.
“We controlled the game a lot better and of course, we're really happy with the three points."
England manager Gareth Southgate was in the stands at the King Power Stadium, where ever-improving Barnes kept his cool to score his 10th goal of the season in all competitions.
“In games, it happens, and the game stretches out," the academy graduate told LCFC TV.
“There's always space late on, especially when they're searching for a late goal, so of course, when you break, you just need to keep your composure and I'm happy to see that one go in.
“As a team, we're scoring a lot of goals this year, and I think I've been a big part of that. I think I'm just a bit more composed in front of goal this year, and of course, that's showing in the goal tally.
“The way we play, we're so attacking, and that suits me perfectly. All our frontmen go into the game thinking they're going to score or get an assist.
“There will be a lot of chances for us, so of course, every game is exciting."