Raphinha' s goal from a direct free-kick put Leeds in the driving seat for all of about 10 seconds before Barnes equalised with a wonderstrike.
Leeds had chances to win the game and Leicester had a goal chalked off for a tight offside call by VAR before they shared the spoils.
It was a difficult encounter for the visitors, who struggled to play out from the back under heavy pressure from the hosts, but Barnes knew what was coming and felt the Foxes stood up to it well.
“You always know that when you play Leeds, it’s going to be about running," he said.
"You’ve got to track runners and you’ve got to dig deep, really. Especially when you have the ball, you know that people are flying everywhere, so [you have to have] a lot of focus in the game and you’ve got to weather their good spells and make sure that we stand strong as a team, and I think we did that.
“Obviously, the goal from the free-kick was a great ball in and we bounced back well with our goal. We got ourselves right back in it, and then I think both teams had chances after that. All in all, it’s probably a fair result."
The entertainment provided throughout the game was noted by both Marcelo Bielsa and Brendan Rodgers after the game and Barnes believes it has a lot to do with the way Leeds set out to play, no matter the identity of the opposition.
“It’s a game where you’re pretty much one-on-one everywhere,” he said.
“You see how they do it week in, week out and they don’t change for any team they play. You know you’ve got a one-on-one duel for pretty much 90 minutes, and if you can get the better of the man, you know your role defensively.
“Every man in the team stuck to it really well and like I said, we had chances and they had chances. It’s always the same with Leeds, it’s going to be an open game.”