The pair were filmed arguing in the tunnel after the half-time whistle.
"It was nothing out the ordinary - just two managers fighting to win a game," Dyche said.
Asked about his side's performance, Dyche added: "We did the basics very well. Diligence to see jobs off. Popey has still had to make good saves. I always believed in the side to find a moment. We had a few. Barnesy got the penalty and slotted it away well.
"There is a way a game works out and you can see the patterns sometimes. You just worry a block lands to their players, it didn't feel like that game. They were probing but our shape and diligence was excellent. The will of the keeper and defenders to keep a clean sheet. And the strikers too. You defend from the front.
"We don't lack belief. We lack a bit of talent sometimes but not belief. When we get it right as a structure and a unit, doing the basics, it keeps you in a game and then you have to find a way to win it.
"We were close to winning here last season. It doesn't mean we will win tonight. But we took on a game plan the best way we could."