Firmino and his team-mate Fabinho were seen embracing United's Fred and Andreas Pereira in the tunnel, with all four players having played for Brazil.
Firmino told ESPN Brazil: "I don't want to create controversy with anyone.
"I find it quite normal before the game to greet each other, ask how they are doing. That's all. Nothing more than that.
"But on the pitch, they aren't friends, each one defends his club to the best of his ability. Then the rivalry increases on the pitch."